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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»
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.
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
Linking options:
https://www.mathnet.ru/eng/im8759https://doi.org/10.1070/IM8759 https://www.mathnet.ru/eng/im/v82/i4/p178
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Abstract page: | 480 | Russian version PDF: | 57 | English version PDF: | 16 | References: | 35 | First page: | 10 |
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