Email this article Grothendieck-Serre duality and theta-invariants on arithmetic surfaces
- Authors: Osipov D.V.1
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Affiliations:
- Steklov Mathematical Institute of Russian Academy of Sciences
- Issue: Vol 487, No 6 (2019)
- Pages: 617-621
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/15951
- DOI: https://doi.org/10.31857/S0869-56524876617-621
- ID: 15951
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Abstract
In the paper, a description of the Grothendieck-Serre duality on an arithmetic surface by means of fixing a horizontal divisor is given and this description is applied to the generalization of theta-invariants.
About the authors
D. V. Osipov
Steklov Mathematical Institute of Russian Academy of Sciences
Author for correspondence.
Email: d_osipov@mi-ras.ru
Russian Federation, 8, Gubkina street, Moscow, 117966
References
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- Hartshorne R. Residues and Duality. Lecture Notes of a Seminar on the Work of A. Grothendieck, Given at Harvard 1963/64. With an Appendix by P. Deligne. Lecture Notes in Mathematics. № 20. B.; N.Y.: Springer-Verlag, 1966.
- Liu Q. Algebraic Geometry and Arithmetic Curves. Translated from the French by Reinie Erné. Oxford Graduate Texts in Mathematics, 6. Oxford Science Publications. Oxford: Oxford University Press, 2002.
- Deligne P. Le Déterminant de la Cohomologie. Current Trends in Arithmetical Algebraic Geometry (Arcata, Calif., 1985), 93-177. Contemp. Math., 67. Amer. Math. Soc., Providence (RI), 1987.
- Осипов Д. В., Паршин А. Н. Гармонический анализ на локальных полях и пространствах аделей // Изв. РАН. Сер. матем. 2011. Т. 75. № 4. С. 91-164.
- Осипов Д. В. Арифметические и адельные факторгруппы // Изв. РАН. Сер. матем. 2018. Т. 82. № 4. С. 178-198.
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