Kurke, Herbert; Osipov, Denis V.; Zheglov, Alexander B. Formal groups arising from formal punctured ribbons. (English) Zbl 1203.14012 Int. J. Math. 21, No. 6, 755-797 (2010). 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. Reviewer: Stefan Schröer (Düsseldorf) Cited in 2 Documents MSC: 14D15 Formal methods and deformations in algebraic geometry 14D20 Algebraic moduli problems, moduli of vector bundles 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) Keywords:formal groups; Picard schemes; two-dimensional local fields PDF BibTeX XML Cite \textit{H. Kurke} et al., Int. J. Math. 21, No. 6, 755--797 (2010; Zbl 1203.14012) Full Text: DOI arXiv References: [1] Artin M., Ann. Sci. Ec. Norm. Super. (4) 10 pp 87– · Zbl 0351.14023 · doi:10.24033/asens.1322 [2] Atiyah M., Introduction to Commutative Algebra (1969) · Zbl 0175.03601 [3] Bass H., Algebraic K-Theory (1968) [4] Bourbaki N., Elements de Math. 31, in: Algebre Commutative (1965) · Zbl 0141.03501 [5] Grothendieck A., Publ. Math. Inst. Hautes. Études. Sci. pp 11– [6] Grothendieck A., Publ. Math. Inst. Hautes. Études. Sci. pp 20– [7] Grothendieck A., Éléments de Géométrie Algébrique I (1971) [8] DOI: 10.1007/978-1-4757-3849-0 · doi:10.1007/978-1-4757-3849-0 [9] Kurke H., J. Reine Angew. Math. 629 pp 133– [10] DOI: 10.1007/BFb0066156 · doi:10.1007/BFb0066156 [11] Milne J., Étale Cohomology (1980) · Zbl 0433.14012 [12] DOI: 10.1081/AGB-100105994 · Zbl 1014.14015 · doi:10.1081/AGB-100105994 [13] DOI: 10.1007/BF02698802 · Zbl 0592.35112 · doi:10.1007/BF02698802 [14] DOI: 10.1007/BF01239518 · Zbl 0794.13008 · doi:10.1007/BF01239518 [15] Zariski O., Commutative Algebra (1975) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.