Arithmetic surfaces and adelic quotient groups

  title={Arithmetic surfaces and adelic quotient groups},
  author={Denis Vasilievich Osipov},
  journal={Izvestiya: Mathematics},
  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. 

Adelic quotient group for algebraic surfaces

  • D. Osipov
  • Mathematics
    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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Eight papers translated from the Russian

On tetragonal curves by S. G. Dalayan On pointwise estimates of some capacity potentials by I. V. Skrypnik Some singular boundary value problems for partial differential equations by V. P. Palamodov