an:05758236
Zbl 1203.14012
Kurke, Herbert; Osipov, Denis V.; Zheglov, Alexander B.
Formal groups arising from formal punctured ribbons
EN
Int. J. Math. 21, No. 6, 755-797 (2010).
00263478
2010
j
14D15 14D20 37K10
formal groups; Picard schemes; two-dimensional local fields
The authors continue their study of so-called ribbons initiated in [J. Reine Angew. Math. 629, 133--170 (2009; Zbl 1168.14002)].
A ribbon consists of an algebraic curve \(C\) over a ground field \(k\), together with sheaf of \(k\)-algebras \(\mathcal{A}\) endowed with a descending filtration \(\mathcal{A}_i\) satisfying certain axioms. The most important examples come from curves lying as Cartier divisors on a surface \(X\), where \(\mathcal{A}_i\) is the ideal sheaf of \(iC\) viewed as a divisor on the formal completion \(\hat{X}\) along the curve.
The authors study the various Picard and Brauer groups for ribbons, determine the respective tangent spaces, and prove some representability results.
Stefan Schr??er (D??sseldorf)
Zbl 1168.14002