منابع مشابه
Local Class Field Theory Contents
1 Wedderburn theory and the Brauer group 2 1.1 Algebras and modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 The Brauer group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Splitting fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Crossed products . . . . . . . . . . . . . . . . ...
متن کاملKato ’ s higher local class field theory
We first recall the classical local class field theory. Let K be a finite extension of Qp or Fq((X)). The main theorem of local class field theory consists of the isomorphism theorem and existence theorem. In this section we consider the isomorphism theorem. An outline of one of the proofs is as follows. First, for the Brauer group Br(K), an isomorphism inv: Br(K) →̃Q/Z is established; it mainly...
متن کاملExplicit higher local class field theory
Consider now an approach based on a generalization [F2] of Neukirch’s approach [N]. Below is a modified system of axioms of class formations (when applied to topological K -groups) which imposes weaker restrictions than the classical axioms (cf. section 11). (A1). There is a Ẑ-extension of F . In the case of higher local fields let F pur/F be the extension which corresponds to K sep 0 /K0: F pu...
متن کاملLocal Class Field Theory via Lubin-Tate Theory
We give a self-contained proof of local class field theory, via Lubin-Tate theory and the Hasse-Arf theorem, refining the arguments of Iwasawa [4].
متن کاملl-ADIC CLASS FIELD THEORY FOR REGULAR LOCAL RINGS
(1.1) cX,D,lr : H n s (XNis,K M n (OX , ID))/l r −→ H s (Xét, j!μ ⊗n lr ) for a prime number l 6= p and r > 0. Here j denotes the natural open immersion X − Supp(D) →֒ X, ID ⊂ OX denotes the defining ideal of D and K M n (OX , ID) denotes a certain Milnor K-sheaf in the Nisnevich topology (see Notation below). We will review the construction of this map in §3. The group H s (XNis,K M n (OX , ID)...
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ژورنال
عنوان ژورنال: St. Petersburg Mathematical Journal
سال: 2004
ISSN: 1061-0022
DOI: 10.1090/s1061-0022-04-00834-9