Higher-dimensional Contou-Carrère symbol and continuous automorphisms

A higher-dimensional Contou-Carrère symbol: local theory

We construct a higher-dimensional Contou-Carrère symbol and we study its various fundamental properties. The higher-dimensional Contou-Carrère symbol is defined by means of the boundary map for $K$-groups. We prove its universal property. We provide an explicit formula for the higher-dimensional Contou-Carrère symbol over $\mathbb Q$ and we prove integrality of this formula. A relation with the higher-dimensional Witt pairing is also studied.

The two-dimensional Contou-Carrère symbol and reciprocity laws

We define a two-dimensional Contou-Carrère symbol, which is a deformation of the two-dimensional tame symbol and is a natural generalization of the (usual) one-dimensional Contou-Carrère symbol. We give several constructions of this symbol and investigate its properties. Using higher categorical methods, we prove reciprocity laws on algebraic surfaces for this symbol. We relate also the two-dimensional Contou-Carrère symbol with the two-dimensional class field theory.

A Generalized Contou-Carrère Symbol and its Reciprocity Laws in Higher Dimensions

We generalize the theory of Contou-Carrère symbols to higher dimensions. To an $(n+1)$-tuple $f_0,\dots,f_n \in A((t_1))\cdots((t_n))^{\times}$, where $A$ denotes a commutative algebra over a field $k$, we associate an element $(f_0,\dots,f_n) \in A^{\times}$, compatible with the higher tame symbol for $k = A$, and earlier constructions for $n = 1$, by Contou-Carrère, and $n = 2$ by Osipov--Zhu. Our definition is based on the notion of \emph{higher commutators} for central extensions of groups by spectra, thereby extending the approach of Arbarello--de Concini--Kac and Anderson--Pablos Romo. F…

On the Contou-Carrere Symbol for Surfaces

This is a preliminary report on the Contou-Carrere symbol for surfaces. It consists of two parts. In the first part, we recall technical results needed to define the symbol. The second part is where we compute all components of the Coutou-Carrere symbol for surfaces, using iterated integrals over membranes.

与迭代洛朗级数代数和更高维Contou-Carrere符号相关的多项乘法映射

Polymultiplicative maps associated with the algebra of Iterated Laurent series and the higher-dimensional Contou-Carrere Symbol

本文研究了从迭代洛朗级数代数到环的多项乘法映射，并证明其与更高维Contou-Carrère符号的关系。

Contou-Carrère符号、德利涅配对与五元组

Contou-Carrère symbol, Deligne pairing and quintets

研究仿射基概型上射影曲线的互反律，其推广了韦伊互反律等。应用互反律描述群ind-概型中心扩张对五元组模栈上线丛的作用，该模栈上线丛由五元组中线丛的德利涅配对构造。