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Izv. RAN. Ser. Mat., 2013, Volume 77, Issue 4, Pages 73–102 (Mi izv8013)  

This article is cited in 1 scientific paper (total in 1 paper)

The unramified two-dimensional Langlands correspondence

D. V. Osipov

Steklov Mathematical Institute of the Russian Academy of Sciences

Abstract: We describe the unramified Langlands correspondence for two-dimensional local fields and construct a categorical analogue of the unramified principal series representation and study its properties. The main tool for this description is the construction of a certain central extension. For this and other central extensions, we prove non-commutative reciprocity laws (that is, splitting of the central extensions over certain subgroups) for arithmetic surfaces and projective surfaces over finite fields. These reciprocity laws connect central extensions constructed locally and globally.

Keywords: 2-vector spaces, two-dimensional local fields, higher adèles, generalized Langlands programme, two-dimensional non-commutative reciprocity laws.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00145-а
11-01-12098-офи-м-2011
12-01-33024 мол_а_вед
Ministry of Education and Science of the Russian Federation НШ-5139.2012.1


DOI: https://doi.org/10.4213/im8013

Full text: PDF file (726 kB)
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English version:
Izvestiya: Mathematics, 2013, 77:4, 714–741

Bibliographic databases:

Document Type: Article
UDC: 512.75+512.585
MSC: 11R37, 14J20, 18D05
Received: 22.06.2012

Citation: D. V. Osipov, “The unramified two-dimensional Langlands correspondence”, Izv. RAN. Ser. Mat., 77:4 (2013), 73–102; Izv. Math., 77:4 (2013), 714–741

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. V. Osipov, “Noncommutative reciprocity laws on algebraic surfaces: the case of tame ramification”, Sb. Math., 204:12 (2013), 1797–1810  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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