Cohomology of topological groups with applications to the Weil group
نویسندگان
چکیده
منابع مشابه
Cohomology of topological groups with applications to the Weil group
We establish various properties of the definition of cohomology of topological groups given by Grothendieck, Artin and Verdier in SGA4, including a Hochschild-Serre spectral sequence and a continuity theorem for compact groups. We use these properties to compute the cohomology of the Weil group of a totally imaginary field, and of the Weil-étale topology of a number ring recently introduced by ...
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We generalize a theorem of Tate and show that the second cohomology of the Weil group of a global or local field with coefficients in C∗ (or, more generally, with coefficients in the complex points of an algebraic torus over C) vanish, where the cohomology groups are defined using measurable cochains in the sense of Moore. We recover a theorem of Labesse stating that the admissible homomorphism...
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in this paper we introduce a new definition of the first non-abelian cohomology of topological groups. we relate the cohomology of a normal subgroup $n$ of a topological group $g$ and the quotient $g/n$ to the cohomology of $g$. we get the inflation-restriction exact sequence. also, we obtain a seven-term exact cohomology sequence up to dimension 2. we give an interpretation of the first non-a...
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We show that three dimensional Chern-Simons gauge theories with a compact gauge group G (not necessarily connected or simply connected) can be classified by the integer cohomology group H(BG,Z). In a similar way, possible Wess-Zumino interactions of such a group G are classified by H(G, Z). The relation between three dimensional Chern-Simons gauge theory and two dimensional sigma models involve...
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2008
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x07003338