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arXiv · 2105.14626

Central extensions and Riemann-Roch theorem on algebraic surfaces

D. V. Osipov
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Abstract

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

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D. V. Osipov. 2021-05-30. Central extensions and Riemann-Roch theorem on algebraic surfaces. https://doi.org/10.1070/sm9623

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