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Izvestiya: Mathematics, 2018, Volume 82, Issue 4, Pages 817–836
DOI: https://doi.org/10.1070/IM8759 (Mi im8759) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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»
English version PDF (376 kB) Citations (2)
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DOI: https://doi.org/10.1070/IM8759
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.
Received: 14.01.2018
Revised: 27.02.2018
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2018, Volume 82, Issue 4, Pages 178–198
DOI: https://doi.org/10.4213/im8759
Bibliographic databases:
Document Type: Article
UDC: 512.75
MSC: 11R56, 14G40, 11G99
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
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  • https://doi.org/10.1070/IM8759
  • https://www.mathnet.ru/eng/im/v82/i4/p178
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    English version PDF:16
    References:35
    First page:10
     
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