Denis Osipov - Academia.edu (original) (raw)

Papers by Denis Osipov

A categorical proof of the Parshin reciprocity laws on algebraic surfaces

Proceedings of the Steklov Institute of Mathematics, 2016

We study continuous homomorphisms between algebras of iterated Laurent series over a commutative ... more We study continuous homomorphisms between algebras of iterated Laurent series over a commutative ring. We give a full description of such homomorphisms in terms of a discrete data determined by the images of parameters. In similar terms, we give a criterion of invertibility of an endomorphism and provide an explicit formula for the inverse endomorphism. We study the behavior of the higher-dimensional residue under continuous homomorphisms.

Matematicheskie Zametki, 2015

Известия Российской академии наук. Серия математическая, 2013

Неразветвленное двумерное соответствие Ленглендса Описано неразветвленное соответствие Ленглендса... more Неразветвленное двумерное соответствие Ленглендса Описано неразветвленное соответствие Ленглендса для двумерных локальных полей, построен категорный аналог неразветвленных представлений основной серии и изучены его свойста. Для этого используется конструкция некоторого центрального расширения, для которого (и других центральных расширений) доказаны некоммутативные законы взаимности (т. е. расщепление центральных расширений над некоторыми подгруппами) для арифметических поверхностей и проективных поверхностей над конечным полем, связывающие центральные расширения, построенные локально и глобально. Библиография: 24 наименования. Ключевые слова: 2-векторные пространства, двумерные локальные поля, высшие адели, обобщение программы Ленглендса, двумерные некоммутативные законы взаимности.

Surveys in Contemporary Mathematics

Известия Российской академии наук. Серия математическая, 2011

Гармонический анализ на локальных полях и пространствах аделей. II Развивается гармонический анал... more Гармонический анализ на локальных полях и пространствах аделей. II Развивается гармонический анализ в некоторых категориях фильтрованных абелевых групп и векторных пространств. Эти категории содержат в качестве объектов локальные поля и пространства аделей, возникающие из арифметических поверхностей. Доказаны структурные теоремы для факторов групп аделей алгебраических и арифметических поверхностей. Библиография: 19 наименований.

Matematicheskie Zametki, 2007

Мы исследуем различные новые свойства и примеры двумерного и одномерного соответствия Кричевера. ... more Мы исследуем различные новые свойства и примеры двумерного и одномерного соответствия Кричевера. Библиография: 16 названий.

Sbornik: Mathematics, 1997

Sbornik: Mathematics, 2003

ABSTRACT

Успехи математических наук, 2013

Математический сборник, 2005

Математический сборник, 1997

Izvestiya: Mathematics, 2001

Izvestiya: Mathematics, 2013

In this paper we describe the unramified Langlands correspondence for twodimensional local fields... more In this paper we describe the unramified Langlands correspondence for twodimensional local fields, we construct a categorical analogue of the unramified principal series representations and study its properties. The main tool for this description is the construction of a central extension. For this (and other) central extension we prove noncommutative reciprocity laws (i.e. the splitting of the central extensions over some subgroups) for arithmetic surfaces and projective surfaces over a finite field. These reciprocity laws connect central extensions which are constructed locally and globally.

Doklady Mathematics, 2011

International Journal of Mathematics, 2007

We consider categories Cn which are very close to the iterated functor [Formula: see text], which... more We consider categories Cn which are very close to the iterated functor [Formula: see text], which was introduced by Beilinson. We prove that an adelic space on n-dimensional Noetherian scheme is an object of Cn.

Russian Mathematical Surveys, 2020

This article contains a survey of a new algebro-geometric approach for working with iterated alge... more This article contains a survey of a new algebro-geometric approach for working with iterated algebraic loop groups associated with iterated Laurent series over arbitrary commutative rings and its applications to the study of the higher-dimensional Contou-Carrère symbol. In addition to the survey, the article also contains new results related to this symbol. The higher-dimensional Contou-Carrère symbol arises naturally when one considers deformation of a flag of algebraic subvarieties of an algebraic variety. The non-triviality of the problem is due to the fact that, in the case , for the group of invertible elements of the algebra of -iterated Laurent series over a ring, no representation is known in the form of an ind-flat scheme over this ring. Therefore, essentially new algebro-geometric constructions, notions, and methods are required. As an application of the new methods used, a description of continuous homomorphisms between algebras of iterated Laurent series over a ring is g...

arXiv: Algebraic Geometry, 2003

We give a construction of the two-dimensional tame symbol as the commutator of a group-like monoi... more We give a construction of the two-dimensional tame symbol as the commutator of a group-like monoidal groupoid which is obtained from some group of k-linear operators acting in a two-dimensional local field and corresponds to some third cohomology class of this group. We give also the hypothetical method for the proof of the two-dimensional Parshin reciprocity laws. This text was written in 2003 as preprint 03-13 of the Humboldt University of Berlin and was available at this http URL (only evident misprints are corrected now). Later E. Frenkel and X. Zhu obtained in arXiv:0810.1487 [math.RT] more general results concerning the third cohomology classes of groups acting on two-dimensional local fields, and the author and X. Zhu obtained in arXiv:1002.4848 [math.AG] the proof of the Parshin reciprocity laws on an algebraic surface similar to the Tate proof of the residue formula on an algebraic curve.