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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.)
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