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Formal groups arising from formal punctured ribbons. (English) Zbl 1203.14012
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.

##### 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
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##### References:
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