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Izv. RAN. Ser. Mat., 2018, Volume 82, Issue 4, Pages 178–198 (Mi izv8759)  

Arithmetic surfaces and adelic quotient groups

D. V. Osipovabc

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b National Research University "Higher School of Economics" (HSE), Moscow
c National University of Science and Technology «MISIS»

Abstract: We explicitly calculate an arithmetic adelic quotient group for a locally free sheaf on an arithmetic surface when the fibre over the infinite point of the base is taken into account. The result is stated in the form of a short exact sequence. We relate the last term of this sequence to the projective limit of groups which are finite direct products of copies of the one-dimensional real torus and are connected with the first cohomology groups of locally free sheaves on the arithmetic surface.

Keywords: arithmetic surface, Parshin–Beilinson adeles, arithmetic adeles.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 14.641.31.0001
The author is partially supported by Laboratory of Mirror Symmetry NRU HSE, RF Government grant, ag. no. 14.641.31.0001.


DOI: https://doi.org/10.4213/im8759

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English version:
Izvestiya: Mathematics, 2018, 82:4, 817–836

Bibliographic databases:

UDC: 512.75
MSC: 11R56, 14G40, 11G99
Received: 14.01.2018
Revised: 27.02.2018

Citation: D. V. Osipov, “Arithmetic surfaces and adelic quotient groups”, Izv. RAN. Ser. Mat., 82:4 (2018), 178–198; Izv. Math., 82:4 (2018), 817–836

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  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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