Arithmetic surfaces and adelic quotient groups

Osipov, D. V.

doi:10.1070/im8759

Cited by 4 publications

(2 citation statements)

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“…Another application of the calculation of adelic quotient group (2) for two-dimensional schemes will be given in the subsequent paper [11]. It will be calculated explicitly an adelic quotient group on an arithmetic surface when the fibres over Archimedean points are taken into account.…”

Section: Introductionmentioning

confidence: 99%

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Adelic quotient group for algebraic surfaces

Osipov

2018

St. Petersburg Math. J.

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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 over a field is given.Recently there were also found the interesting connections and interactions with many questions between the higher adeles theory and the Langlands program, see [16].As an application, we deduce from our calculations of adelic quotient group (2) the corresponding quotient group when X is a projective irreducible normal surface over a field k , and C is the support of an ample divisor. As in the one-dimensional case, this quotient group will be a linearly compact k -vector space. We note that this quotient group when the surface X is smooth and the sheaf F = O X was calculated in [12, § 14].

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Section: Introductionmentioning

confidence: 99%

“…This will be justified by explicit calculations with arithmetic adeles on arithmetic surfaces in [11]. (Arithmetic adeles, i.e.…”

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confidence: 99%