Arithmetic surfaces and adelic quotient groups

@article{Osipov2018ArithmeticSA,
  title={Arithmetic surfaces and adelic quotient groups},
  author={Denis Vasilievich Osipov},
  journal={Izvestiya: Mathematics},
  year={2018},
  volume={82},
  pages={817 - 836}
}
  • D. Osipov
  • Published 8 January 2018
  • Mathematics
  • Izvestiya: Mathematics
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. 
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Adelic quotient group for algebraic surfaces

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    St. Petersburg Mathematical Journal
  • 2018
We calculate explicitly an adelic quotient group for an excellent Noetherian normal integral two-dimensional separated scheme. An application to an irreducible normal projective algebraic surface…

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