|
Zapiski Nauchnykh Seminarov POMI, 2014, Volume 430, Pages 53–60
(Mi znsl6082)
|
|
|
|
This article is cited in 3 scientific papers (total in 3 papers)
Explicit form of Hilbert symbol for polynomial formal groups over multidimensional local field. I
S. V. Vostokov, V. V. Volkov, M. V. Bondarko St. Petersburg State University, St. Petersburg, Russia
Abstract:
Let $K$ be a multidimensional local field with characteristic different from characteristic of its residue field, $c$ be a unit of $K$ and $F_c(X,Y)=X+Y+cXY$ be a polynomial formal group, which defines formal module $F_c(\mathfrak M)$ over maximal ideal of ring of integers in $K$. Assume that $K$ contains group of the roots of isogeny $[p^m]_c(X)$, which we denote by $\mu_{F_c,m}$. Let $\mathcal H$ be the multiplicative group of Cartier curves and $\mathcal H_c$ be a formal analogue of the module $F_c(\mathfrak M)$. In the current work we construct formal symbol $\{\cdot,\cdot\}_c\colon K_n(\mathcal H)\times\mathcal H_c\to\mu_{F_c,m}$ and check its basic properties. This is the first step in construction of the explicit formula for the Hilbert symbol.
Key words and phrases:
Hilbert symbol, multidimensional local field, formal groups, polynomial formal groups.
Received: 30.09.2014
Citation:
S. V. Vostokov, V. V. Volkov, M. V. Bondarko, “Explicit form of Hilbert symbol for polynomial formal groups over multidimensional local field. I”, Problems in the theory of representations of algebras and groups. Part 27, Zap. Nauchn. Sem. POMI, 430, POMI, St. Petersburg, 2014, 53–60; J. Math. Sci. (N. Y.), 219:3 (2016), 370–374
Linking options:
https://www.mathnet.ru/eng/znsl6082 https://www.mathnet.ru/eng/znsl/v430/p53
|
Statistics & downloads: |
Abstract page: | 291 | Full-text PDF : | 92 | References: | 33 |
|