Reconstructing function fields from Milnor K-theory
نویسندگان
چکیده
منابع مشابه
Milnor K-theory of smooth quasiprojective varieties
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 ...
متن کاملMilnor K-theory of smooth varieties
Let k be a field and X a smooth projective variety of dimension d over k. Generalizing a construction of Kato and Somekawa, we define a Milnortype group Ks(k; CH0(X);Gm) which is isomorphic to the ordinary Milnor K-group Km s (k) in the case X = Spec k. We prove that Ks(k; CH0(X);Gm) is isomorphic to both the higher Chow group CHd+s(X, s) and the Zariski cohomology group Hd Zar(X,K d+s).
متن کاملGalois Module Structure of Milnor K - Theory
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...
متن کامل6. Topological Milnor K -groups of higher local fields
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...
متن کاملMilnor K-groups and Function Fields of Hypersurfaces in Positive Characteristic
Let X be an integral affine or projective hypersurface over a field F of characteristic p > 0, and let F (X) denote its function field. In a recent article, Dolphin and Hoffmann obtained an explicit description of the kernel of the natural restriction homomorphism between the rings of absolute Kähler differentials of F and F (X), respectively. In this note, we examine the possibility of derivin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Algebra & Number Theory
سال: 2021
ISSN: ['1944-7833', '1937-0652']
DOI: https://doi.org/10.2140/ant.2021.15.2261