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## Gille, Philippe

Compute Distance To:
 Author ID: gille.philippe Published as: Gille, P.; Gille, Ph.; Gille, Philippe
 Documents Indexed: 58 Publications since 1981, including 6 Books
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#### Co-Authors

 25 single-authored 6 Pianzola, Arturo 3 Colliot-Thélène, Jean-Louis 2 Beli, Constantin-Nicolae 2 Edixhoven, Bas 2 Lee, Ting-Yu 2 Moret-Bailly, Laurent 2 Parimala, Raman 2 Polo, Patrick 2 Prasad, Gopal 2 Quéguiner-Mathieu, Anne 2 Szamuely, Tamás 1 Borovoi, Mikhail V. 1 Chernousov, Vladimir I. 1 Gabber, Ofer 1 Garibaldi, Skip 1 Kunyavskiĭ, Boris Èmmanuilovich 1 Loute, Etienne 1 Reichstein, Zinovy B. 1 Semenov, Nikita
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#### Serials

 2 Canadian Mathematical Bulletin 2 Commentarii Mathematici Helvetici 2 Compositio Mathematica 2 Duke Mathematical Journal 2 Journal of Algebra 2 Comptes Rendus de l’Académie des Sciences. Série I 2 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 2 Cambridge Studies in Advanced Mathematics 2 Panoramas et Synthèses 1 Publications Mathématiques 1 Journal of the London Mathematical Society. Second Series 1 Journal of Mathematics of Kyoto University 1 Journal of Number Theory 1 Journal of Pure and Applied Algebra 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Annalen 1 Mathematica Scandinavica 1 Memoirs of the American Mathematical Society 1 Pacific Journal of Mathematics 1 Rendiconti del Seminario Matematico della Università di Padova 1 Transactions of the American Mathematical Society 1 $$K$$-Theory 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 Journal of Group Theory 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Pure and Applied Mathematics Quarterly 1 Lecture Notes in Mathematics 1 Proceedings of the Steklov Institute of Mathematics 1 Algebra & Number Theory 1 Algebraic Geometry
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#### Fields

 31 Algebraic geometry (14-XX) 29 Group theory and generalizations (20-XX) 19 Number theory (11-XX) 9 Field theory and polynomials (12-XX) 7 Nonassociative rings and algebras (17-XX) 6 $$K$$-theory (19-XX) 5 Associative rings and algebras (16-XX) 2 General and overarching topics; collections (00-XX) 2 Commutative algebra (13-XX) 1 Combinatorics (05-XX) 1 Category theory; homological algebra (18-XX) 1 Topological groups, Lie groups (22-XX) 1 Potential theory (31-XX) 1 Geometry (51-XX) 1 Numerical analysis (65-XX) 1 Operations research, mathematical programming (90-XX)

#### Citations contained in zbMATH

50 Publications have been cited 494 times in 350 Documents Cited by Year
Central simple algebras and Galois cohomology. Zbl 1137.12001
Gille, Philippe; Szamuely, Tamás
2006
Arithmetic of linear algebraic groups over 2-dimensional geometric fields. Zbl 1129.11014
Colliot-Thélène, J.-L.; Gille, P.; Parimala, R.
2004
Galois cohomology and forms of algebras over Laurent polynomial rings. Zbl 1131.11070
Gille, Philippe; Pianzola, Arturo
2007
The $$R$$-equivalence on reductive algebraic groups defined over a global field. Zbl 0943.20044
Gille, Philippe
1997
The Kneser-Tits problem. Zbl 1198.20038
Gille, Philippe
2009
Isotriviality and étale cohomology of Laurent polynomial rings. Zbl 1132.14042
Gille, Philippe; Pianzola, Arturo
2008
Galois cohomology of quasi-split groups over fields of cohomological dimension $$\leqslant 2$$. Zbl 1017.11019
Gille, Philippe
2001
Rost’s cohomological invariants in positive characteristic. Zbl 0993.20031
Gille, Philippe
2000
Arithmetical birational invariants of linear algebraic groups over two-dimensional geometric fields. Zbl 1057.11023
Borovoi, Mikhail; Kunyavskii, Boris; Gille, Philippe
2004
Central simple algebras and Galois cohomology. 2nd revised and updated edition. Zbl 1373.19001
Gille, Philippe; Szamuely, Tamás
2017
Algebraic actions of arithmetic groups. Zbl 1317.14101
Gille, Philippe; Moret-Bailly, Laurent
2013
Torsors over the punctured affine line. Zbl 1279.14059
Chernousov, V.; Gille, P.; Pianzola, A.
2012
Torsors on the affine line. Zbl 1062.14061
Gille, P.
2002
Resolving $$G$$-torsors by abelian base extensions. Zbl 1157.14311
Chernousov, V.; Gille, P.; Reichstein, Z.
2006
Torsors, reductive group schemes and extended affine Lie algebras. Zbl 1354.17017
Gille, Philippe; Pianzola, Arturo
2013
Conjugacy theorems for loop reductive group schemes and Lie algebras. Zbl 1377.14011
Chernousov, V.; Gille, P.; Pianzola, A.
2014
Algebraic groups with few subgroups. Zbl 1183.20053
Garibaldi, Skip; Gille, Philippe
2009
Reduction of structure for torsors over semilocal rings. Zbl 1157.14028
Chernousov, V.; Gille, P.; Reichstein, Z.
2008
Isotriviality of torsors over Laurent polynomial rings. Zbl 1107.14035
Gille, Philippe; Pianzola, Arturo
2005
Unipotent subgroups of reductive groups in characteristic $$p>0$$. Zbl 1013.20040
Gille, Philippe
2002
Examples of non-rational varieties of adjoint groups. Zbl 0911.14026
Gille, Philippe
1997
Serre’s conjecture. II: A survey. Zbl 1239.11046
Gille, Philippe
2010
A lower bound on the essential dimension of a connected linear group. Zbl 1173.11022
Gille, Philippe; Reichstein, Zinovy
2009
Type of maximal tori of semisimple groups. Zbl 1193.20057
Gille, P.
2004
On the classification of semisimple group schemes. Zbl 1356.14035
Gille, Philippe
2015
Principal bundles over Henselian valued fields. Zbl 1322.14068
Gabber, Ofer; Gille, Philippe; Moret-Bailly, Laurent
2014
Remarks on weak approximation over a function field of one variable. Zbl 1201.11066
Colliot-Thélène, Jean-Louis; Gille, Philippe
2004
$$R$$- equivalence and norm principle in Galois cohomology. Zbl 0826.12003
Gille, Philippe
1993
A classification of torsors over Laurent polynomial rings. Zbl 1362.14022
Chernousov, Vladimir; Gille, Philippe; Pianzola, Arturo
2017
Specialisation of the $$R$$-equivalence for the reductive groups. Zbl 1067.20063
Gille, Philippe
2004
Examples of algebraic groups of type $$G_2$$ having the same maximal tori. Zbl 1356.20028
Beli, Constantin; Gille, P.; Lee, Ting-Yu
2016
Octonion algebras over rings are not determined by their norms. Zbl 1358.11126
Gille, Philippe
2014
Formula for the Rost invariant. Zbl 1262.11050
Gille, Philippe; Quéguiner-Mathieu, Anne
2011
The wild fundamental group of an affine group in characteristic $$p>0$$. Zbl 0978.14034
Gille, Philippe
2000
An arithmetic finiteness theorem on reductive groups. Zbl 0806.20036
Gille, Philippe
1993
Isotopes of octonion algebras, $$\mathbf{G}_{2}$$-torsors and triality. Zbl 1452.17031
Alsaody, S.; Gille, P.
2019
On maximal tori of algebraic groups of type $$G_2$$. Zbl 1356.20029
Beli, Constantin; Gille, Philippe; Lee, Ting-Yu
2015
Examples of anisotropic simply connected semi-simple groups containing an unipotent subgroup. Zbl 1284.11067
Gille, Philippe; Quéguiner-Mathieu, Anne
2013
Central simple algebras of degree 5 and $$E_8$$. Zbl 1021.16008
Gille, Philippe
2002
$$R$$-equivalence of $$G$$-coverings over non-Archimedean local fields. Zbl 1078.14531
Gille, Philippe
2001
Arithmetic of linear algebraic groups over certain fields of dimension two. Zbl 1037.20050
Colliot-Thélène, Jean-Louis; Gille, Philippe; Parimala, Raman
2001
Unipotent elements of semisimple simply connected algebraic groups in characteristic $$p>0$$. Zbl 1003.20042
Gille, Philippe
1999
Semi-simple algebraic groups in cohomological dimension $$\leq 2$$. With a comprehensive introduction in English. Zbl 1428.14001
Gille, Philippe
2019
Three-point Lie algebras and Grothendieck’s dessins d’enfants. Zbl 1406.17027
Chernousov, V.; Gille, P.; Pianzola, A.
2016
On group schemes. A celebration of SGA3. Lecture notes of the summer school “Group schemes, an introduction to the SGA3 seminar of Demazure-Grothendieck”, CIRM, Luminy, France, August 29 – September 9, 2011. Volume II. Zbl 1339.14001
Edixhoven, Bas (ed.); Gille, Philippe (ed.); Prasad, Gopal (ed.); Polo, Patrick (ed.)
2015
A cohomological proof of Peterson-Kac’s theorem on conjugacy of Cartan subalgebras for affine Kac-Moody Lie algebras. Zbl 1345.17016
Chernousov, V.; Gille, P.; Pianzola, A.; Yahorau, U.
2014
Zero-cycles on projective varieties and the norm principle. Zbl 1196.14011
Gille, Philippe; Semenov, Nikita
2010
An invariant of elements of finite order in semisimple simply connected algebraic groups. Zbl 1006.20038
Gille, Philippe
2002
Bruhat-Tits decomposition and Hasse principle. Zbl 0983.12002
Gille, Philippe
2000
A basis factorization technique for staircase linear programs. Zbl 0538.90050
Gille, Philippe; Loute, Etienne
1981
Isotopes of octonion algebras, $$\mathbf{G}_{2}$$-torsors and triality. Zbl 1452.17031
Alsaody, S.; Gille, P.
2019
Semi-simple algebraic groups in cohomological dimension $$\leq 2$$. With a comprehensive introduction in English. Zbl 1428.14001
Gille, Philippe
2019
Central simple algebras and Galois cohomology. 2nd revised and updated edition. Zbl 1373.19001
Gille, Philippe; Szamuely, Tamás
2017
A classification of torsors over Laurent polynomial rings. Zbl 1362.14022
Chernousov, Vladimir; Gille, Philippe; Pianzola, Arturo
2017
Examples of algebraic groups of type $$G_2$$ having the same maximal tori. Zbl 1356.20028
Beli, Constantin; Gille, P.; Lee, Ting-Yu
2016
Three-point Lie algebras and Grothendieck’s dessins d’enfants. Zbl 1406.17027
Chernousov, V.; Gille, P.; Pianzola, A.
2016
On the classification of semisimple group schemes. Zbl 1356.14035
Gille, Philippe
2015
On maximal tori of algebraic groups of type $$G_2$$. Zbl 1356.20029
Beli, Constantin; Gille, Philippe; Lee, Ting-Yu
2015
On group schemes. A celebration of SGA3. Lecture notes of the summer school “Group schemes, an introduction to the SGA3 seminar of Demazure-Grothendieck”, CIRM, Luminy, France, August 29 – September 9, 2011. Volume II. Zbl 1339.14001
Edixhoven, Bas (ed.); Gille, Philippe (ed.); Prasad, Gopal (ed.); Polo, Patrick (ed.)
2015
Conjugacy theorems for loop reductive group schemes and Lie algebras. Zbl 1377.14011
Chernousov, V.; Gille, P.; Pianzola, A.
2014
Principal bundles over Henselian valued fields. Zbl 1322.14068
Gabber, Ofer; Gille, Philippe; Moret-Bailly, Laurent
2014
Octonion algebras over rings are not determined by their norms. Zbl 1358.11126
Gille, Philippe
2014
A cohomological proof of Peterson-Kac’s theorem on conjugacy of Cartan subalgebras for affine Kac-Moody Lie algebras. Zbl 1345.17016
Chernousov, V.; Gille, P.; Pianzola, A.; Yahorau, U.
2014
Algebraic actions of arithmetic groups. Zbl 1317.14101
Gille, Philippe; Moret-Bailly, Laurent
2013
Torsors, reductive group schemes and extended affine Lie algebras. Zbl 1354.17017
Gille, Philippe; Pianzola, Arturo
2013
Examples of anisotropic simply connected semi-simple groups containing an unipotent subgroup. Zbl 1284.11067
Gille, Philippe; Quéguiner-Mathieu, Anne
2013
Torsors over the punctured affine line. Zbl 1279.14059
Chernousov, V.; Gille, P.; Pianzola, A.
2012
Formula for the Rost invariant. Zbl 1262.11050
Gille, Philippe; Quéguiner-Mathieu, Anne
2011
Serre’s conjecture. II: A survey. Zbl 1239.11046
Gille, Philippe
2010
Zero-cycles on projective varieties and the norm principle. Zbl 1196.14011
Gille, Philippe; Semenov, Nikita
2010
The Kneser-Tits problem. Zbl 1198.20038
Gille, Philippe
2009
Algebraic groups with few subgroups. Zbl 1183.20053
Garibaldi, Skip; Gille, Philippe
2009
A lower bound on the essential dimension of a connected linear group. Zbl 1173.11022
Gille, Philippe; Reichstein, Zinovy
2009
Isotriviality and étale cohomology of Laurent polynomial rings. Zbl 1132.14042
Gille, Philippe; Pianzola, Arturo
2008
Reduction of structure for torsors over semilocal rings. Zbl 1157.14028
Chernousov, V.; Gille, P.; Reichstein, Z.
2008
Galois cohomology and forms of algebras over Laurent polynomial rings. Zbl 1131.11070
Gille, Philippe; Pianzola, Arturo
2007
Central simple algebras and Galois cohomology. Zbl 1137.12001
Gille, Philippe; Szamuely, Tamás
2006
Resolving $$G$$-torsors by abelian base extensions. Zbl 1157.14311
Chernousov, V.; Gille, P.; Reichstein, Z.
2006
Isotriviality of torsors over Laurent polynomial rings. Zbl 1107.14035
Gille, Philippe; Pianzola, Arturo
2005
Arithmetic of linear algebraic groups over 2-dimensional geometric fields. Zbl 1129.11014
Colliot-Thélène, J.-L.; Gille, P.; Parimala, R.
2004
Arithmetical birational invariants of linear algebraic groups over two-dimensional geometric fields. Zbl 1057.11023
Borovoi, Mikhail; Kunyavskii, Boris; Gille, Philippe
2004
Type of maximal tori of semisimple groups. Zbl 1193.20057
Gille, P.
2004
Remarks on weak approximation over a function field of one variable. Zbl 1201.11066
Colliot-Thélène, Jean-Louis; Gille, Philippe
2004
Specialisation of the $$R$$-equivalence for the reductive groups. Zbl 1067.20063
Gille, Philippe
2004
Torsors on the affine line. Zbl 1062.14061
Gille, P.
2002
Unipotent subgroups of reductive groups in characteristic $$p>0$$. Zbl 1013.20040
Gille, Philippe
2002
Central simple algebras of degree 5 and $$E_8$$. Zbl 1021.16008
Gille, Philippe
2002
An invariant of elements of finite order in semisimple simply connected algebraic groups. Zbl 1006.20038
Gille, Philippe
2002
Galois cohomology of quasi-split groups over fields of cohomological dimension $$\leqslant 2$$. Zbl 1017.11019
Gille, Philippe
2001
$$R$$-equivalence of $$G$$-coverings over non-Archimedean local fields. Zbl 1078.14531
Gille, Philippe
2001
Arithmetic of linear algebraic groups over certain fields of dimension two. Zbl 1037.20050
Colliot-Thélène, Jean-Louis; Gille, Philippe; Parimala, Raman
2001
Rost’s cohomological invariants in positive characteristic. Zbl 0993.20031
Gille, Philippe
2000
The wild fundamental group of an affine group in characteristic $$p>0$$. Zbl 0978.14034
Gille, Philippe
2000
Bruhat-Tits decomposition and Hasse principle. Zbl 0983.12002
Gille, Philippe
2000
Unipotent elements of semisimple simply connected algebraic groups in characteristic $$p>0$$. Zbl 1003.20042
Gille, Philippe
1999
The $$R$$-equivalence on reductive algebraic groups defined over a global field. Zbl 0943.20044
Gille, Philippe
1997
Examples of non-rational varieties of adjoint groups. Zbl 0911.14026
Gille, Philippe
1997
$$R$$- equivalence and norm principle in Galois cohomology. Zbl 0826.12003
Gille, Philippe
1993
An arithmetic finiteness theorem on reductive groups. Zbl 0806.20036
Gille, Philippe
1993
A basis factorization technique for staircase linear programs. Zbl 0538.90050
Gille, Philippe; Loute, Etienne
1981
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#### Cited by 313 Authors

 51 Journal of Algebra 23 Transactions of the American Mathematical Society 22 Journal of Pure and Applied Algebra 14 Advances in Mathematics 14 Transformation Groups 11 Journal of Number Theory 9 Communications in Algebra 9 Israel Journal of Mathematics 9 Duke Mathematical Journal 9 Manuscripta Mathematica 9 Mathematische Annalen 9 Mathematische Zeitschrift 9 Journal de Théorie des Nombres de Bordeaux 8 Inventiones Mathematicae 8 Journal of Algebraic Geometry 7 Archiv der Mathematik 7 Compositio Mathematica 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Journal of Mathematical Sciences (New York) 5 Publications Mathématiques 5 Proceedings of the American Mathematical Society 5 Journal of the American Mathematical Society 4 Proceedings of the Japan Academy. Series A 4 Proceedings of the Steklov Institute of Mathematics 4 European Journal of Mathematics 3 Annales de l’Institut Fourier 3 Central European Journal of Mathematics 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Bulletin de la Société Mathématique de France 2 Canadian Mathematical Bulletin 2 Commentarii Mathematici Helvetici 2 Journal für die Reine und Angewandte Mathematik 2 Pacific Journal of Mathematics 2 Proceedings of the London Mathematical Society. Third Series 2 Bulletin of the American Mathematical Society. New Series 2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 St. Petersburg Mathematical Journal 2 Advances in Applied Clifford Algebras 2 Documenta Mathematica 2 Algebras and Representation Theory 2 Journal of the Institute of Mathematics of Jussieu 2 Algebra & Number Theory 2 Journal of $$K$$-Theory 2 Bulletin of Mathematical Sciences 2 Forum of Mathematics, Sigma 1 American Mathematical Monthly 1 Mathematical Notes 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Arkiv för Matematik 1 Acta Arithmetica 1 Illinois Journal of Mathematics 1 The Journal of Symbolic Logic 1 Mathematische Nachrichten 1 Memoirs of the American Mathematical Society 1 Michigan Mathematical Journal 1 Nagoya Mathematical Journal 1 Revista de la Unión Matemática Argentina 1 Transactions of the Moscow Mathematical Society 1 Advances in Applied Mathematics 1 Computers & Operations Research 1 Forum Mathematicum 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Linear Algebra and its Applications 1 Journal of Algebraic Combinatorics 1 Applied Categorical Structures 1 Bulletin des Sciences Mathématiques 1 Izvestiya: Mathematics 1 Vietnam Journal of Mathematics 1 Journal of Group Theory 1 Annals of Mathematics. Second Series 1 Communications in Contemporary Mathematics 1 Algebraic & Geometric Topology 1 Journal of Algebra and its Applications 1 International Journal of Number Theory 1 Journal of Noncommutative Geometry 1 Journal of Homotopy and Related Structures 1 Science China. Mathematics 1 Afrika Matematika 1 Research in the Mathematical Sciences 1 Open Mathematics
 194 Algebraic geometry (14-XX) 146 Number theory (11-XX) 120 Group theory and generalizations (20-XX) 81 Associative rings and algebras (16-XX) 62 Field theory and polynomials (12-XX) 48 Nonassociative rings and algebras (17-XX) 31 $$K$$-theory (19-XX) 21 Category theory; homological algebra (18-XX) 13 Topological groups, Lie groups (22-XX) 12 Commutative algebra (13-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 5 Algebraic topology (55-XX) 3 Mathematical logic and foundations (03-XX) 3 Geometry (51-XX) 3 Manifolds and cell complexes (57-XX) 2 Ordinary differential equations (34-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Computer science (68-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Measure and integration (28-XX) 1 Numerical analysis (65-XX) 1 Quantum theory (81-XX) 1 Operations research, mathematical programming (90-XX) 1 Information and communication theory, circuits (94-XX)