Email this article Central extensions and the Riemann-Roch theorem on algebraic surfaces
- Authors: Osipov D.V.1,2,3
-
Affiliations:
- Steklov Mathematical Institute of Russian Academy of Sciences
- HSE University
- National University of Science and Technology «MISIS»
- Issue: Vol 213, No 5 (2022)
- Pages: 101-125
- Section: Articles
- URL: https://journal-vniispk.ru/0368-8666/article/view/133450
- DOI: https://doi.org/10.4213/sm9623
- ID: 133450
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Abstract
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.
About the authors
Denis Vasilievich Osipov
Steklov Mathematical Institute of Russian Academy of Sciences; HSE University; National University of Science and Technology «MISIS»
Email: d_osipov@mi-ras.ru
Doctor of physico-mathematical sciences, no status
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