Denis Vasilievich Osipov

On some questions related to the Krichever correspondence

We investigate various new properties and examples of the two-dimensional and one-dimensional Krichever correspondence.

A higher-dimensional Contou-Carrère symbol: local theory

We construct a higher-dimensional Contou-Carr`ere symbol and we study its various fundamental properties. The higher-dimensional Contou-Carr`ere symbol is defined by means of the boundary map for

Formal punctured ribbons and two-dimensional local fields

K

Formal Groups Arising from Formal Punctured Ribbons

-groups. We prove its universal property. We provide an explicit formula for the higher-dimensional Contou-Carr`ere symbol over

Adele constructions of direct images of differentials and symbols

mathbb Q

Многомерный символ Конту-Каррера: локальная теория@@@Higher Contou-Carrère symbol: local theory

and we prove integrality of this formula. A relation with the higher-dimensional Witt pairing is also studied.

Соответствие Кричевера для алгебраических многообразий@@@Krichever correspondence for algebraic varieties

Abstract We investigate formal ribbons on curves. Roughly speaking, formal ribbon is a family of locally linearly compact vector spaces on a curve. We establish a one-to-one correspondence between formal ribbons on curves plus some geometric data and some subspaces of two-dimensional local fields.

Явная формула для многомерного символа Конту - Каррера@@@Explicit formula for the higher-dimensional Contou - Carrére symbol

We investigate the Picard functor of a formal punctured ribbon. We prove that under some conditions this functor is representable by a formal group scheme.