Неразветвленное Двумерное Соответствие Ленглендса

We prove non-commutative reciprocity laws on an algebraic surface defined over a perfect field. These reciprocity laws claim the splittings of some central extensions of globally constructed groups over some subgroups constructed by points or projective curves on a surface. For a two-dimensional local field with a finite last residue field the constructed local central extension is isomorphic to a central extension which comes from the case of tame ramification of the Abelian two-dimensional local Langlands correspondence suggested by M. Kapranov.

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Central extensions and the Riemann-Roch theorem on algebraic surfaces

Osipov

2022

Sb. Math.

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We study canonical central extensions of the general linear group over the ring of adeles on a smooth projective algebraic surface $X$ by means of the group of integers. Via these central extensions and the adelic transition matrices of a rank $n$ locally free sheaf of $\mathcal{O}_X$-modules we obtain a local (adelic) decomposition for the difference of Euler characteristics of this sheaf and the sheaf $\mathcal{O}_X^n$. Two distinct calculations of this difference lead to the Riemann-Roch theorem on $X$ (without Noether's formula). Bibliography: 21 titles.

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Неразветвленное Двумерное Соответствие Ленглендса

Cited by 7 publications

References 23 publications

Tetrahedron equation: algebra, topology, and integrability

Tetrahedron equation: algebra, topology, and integrability

Noncommutative reciprocity laws on algebraic surfaces: the case of tame ramification

Central extensions and the Riemann-Roch theorem on algebraic surfaces

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