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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.

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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