Compatible valuations and generalized Milnor $K$-theory
نویسندگان
چکیده
منابع مشابه
Quotients of Milnor K-rings, Orderings, and Valuations
We define and study the Milnor K-ring of a field F modulo a subgroup of the multiplicative group of F . We compute it in several arithmetical situations, and study the reflection of orderings and valuations in this ring. Introduction Let F be a field and let F× be its multiplicative group. The Milnor K-ring K ∗ (F ) of F is the tensor (graded) algebra of the Z-module F× modulo the homogenous id...
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Let k be a field. Among the algebraic invariants associated to k are the Milnor Kgroups, one for each integer n ≥ 0. These abelian groups were first defined (but not so named) by Milnor in the context of quadratic forms [Mi]. The definition is completely algebraic; nevertheless, a beautiful geometric connection with Bloch’s higher Chow groups was discovered by Nesterenko-Suslin [NS] and Totaro ...
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Let E be a cyclic extension of pth-power degree of a field F of characteristic p. For all m, s ∈ N, we determine KmE/p sKmE as a (Z/pZ)[Gal(E/F )]-module. We also provide examples of extensions for which all of the possible nonzero summands in the decomposition are indeed nonzero. Let F be a field of characteristic p. Let KmF denote the mth Milnor K-group of F and kmF = KmF/pKmF . (See, for ins...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2007
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-07-04132-3