Noncommutative reciprocity laws on algebraic surfaces: the case of tame ramification
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Publication:5412841
DOI10.1070/SM2013V204N12ABEH004360zbMATH Open1326.11033arXiv1307.1995MaRDI QIDQ5412841
Publication date: 28 April 2014
Published in: Sbornik: Mathematics (Search for Journal in Brave)
Abstract: We prove non-commutative reciprocity laws on an algebraic surface defined over a perfect field. These reciprocity laws claim the splittings of some central extensions of globally constructed groups over some subgroups constructed by points or projective curves on a surface. For a two-dimensional local field with a finite last residue field the constructed local central extension is isomorphic to a central extension which comes from the case of tame ramification of the Abelian two-dimensional local Langlands correspondence suggested by M. Kapranov.
Full work available at URL: https://arxiv.org/abs/1307.1995
Geometric class field theory (11G45) Other nonalgebraically closed ground fields in algebraic geometry (14G27) Adèle rings and groups (11R56)
Related Items (2)
A categorical proof of the Parshin reciprocity laws on algebraic surfaces ⋮ Non-abelian Reciprocity Laws on a Riemann Surface
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