Milnor K-Groups and Finite Field Extensions
نویسندگان
چکیده
منابع مشابه
A Regulator Formula for Milnor K-groups
The classical Abel–Jacobi map is used to geometrically motivate the construction of regulator maps from Milnor K-groups KM n (C(X)) to Deligne cohomology. These maps are given in terms of some new, explicit (n − 1)-currents, higher residues of which are defined and related to polylogarithms. We study their behavior in families Xs and prove a rigidity result for the regulator image of the Tame k...
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If R is a smooth semi-local algebra of geometric type over an infinite field, we prove that the Milnor K-group K n (R) surjects onto the higher Chow group CHn(R , n) for all n 0. Our proof shows moreover that there is an algorithmic way to represent any admissible cycle in CHn(R , n) modulo equivalence as a linear combination of “symbolic elements” defined as graphs of units in R. As a byproduc...
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In the paper [Som90] p.105, Somekawa conjectures that his Milnor Kgroup K(k, G1, . . . , Gr) attached to semi-abelian varieties G1,. . . ,Gr over a field k is isomorphic to ExtrMk (Z, G1[−1] ⊗ . . . ⊗ Gr[−1]) where Mk is a certain category of motives over k. The purpose of this note is to give remarks on this conjecture, when we take Mk as Voevodsky’s category of motives DM (k) .
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Let F = Kn, . . . ,K0 = Fq be an n-dimensional local field. We use the notation of section 1. In this section we describe properties of certain quotients K top(F ) of the Milnor K -groups of F by using in particular topological considerations. This is an updated and simplified summary of relevant results in [F1–F5]. Subsection 6.1 recalls wellknown results on K -groups of classical local fields...
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DEFINITION. A group G is called a universal locally finite central extension of A provided that the following conditions are satisfied. (i) A <= (G (the centre of G). (ii) G is locally finite. (iii) (/1-injectivity). Suppose that A <= B <= D with A a (D, that D/A is finite, and that q>: B -> G is an ^-isomorphism (that is, q>{a) = a for all as A). Then there exists an extension q>: D -*• G of (...
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ژورنال
عنوان ژورنال: K-Theory
سال: 2002
ISSN: 1573-0514,0920-3036
DOI: 10.1023/a:1021651617868