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Remarks on Galois cohomology and definability
Journal of Symbolic Logic, 1997In this paper we develop some basic features of Galois cohomology, specifically the connection between first Galois cohomology groups and principal homogeneous spaces, in a model-theoretic context. “Descent theory” also fits into our approach.The model theory involved is elementary, and the reader is referred to [2].
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2009
For a connected reductive group G over F, let Ĝ denote the algebraic group over C, which is the connected component of the Langlands L-group of G. Consider the category of reductive groups over F, whose morphisms are the group homomorphism G → H, which are defined over F.
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For a connected reductive group G over F, let Ĝ denote the algebraic group over C, which is the connected component of the Langlands L-group of G. Consider the category of reductive groups over F, whose morphisms are the group homomorphism G → H, which are defined over F.
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COHOMOLOGICAL DIMENSION OF SOME GALOIS GROUPS
Mathematics of the USSR-Izvestiya, 1975Suppose that is a prime number, is an algebraic number field containing a primitive root ( if ), is a finite set of places of which contains all divisors of , is the maximal -extension of unramified outside , is an arbitrary -extension of , and . In this paper we find necessary and sufficient conditions for the group to be a free pro--group.
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1987
Central to the proof of the Mordell theorem is the idea of descent which was present in the criterion for a group to be finitely generated, see 6(1.4). This criterion was based on the existence of a norm which came out of the theory of heights and the finiteness of the index (E(Q) :2E(Q)), or more generally (E(k) : nE(k)). In this chapter we will study
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Central to the proof of the Mordell theorem is the idea of descent which was present in the criterion for a group to be finitely generated, see 6(1.4). This criterion was based on the existence of a norm which came out of the theory of heights and the finiteness of the index (E(Q) :2E(Q)), or more generally (E(k) : nE(k)). In this chapter we will study
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Applications of Galois Cohomology
1981The theme of this chapter is the use of Galois theory for extending the structure theory of algebraic groups. The applicability of Galois theory stems from the fact that solvable algebraic groups are made up from the additive and multiplicative groups of the base field, and Section 1 provides the technical preparations for exploiting this.
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1997
This § is devoted to the illustration of a “general principle”, which can be stated roughly as follows:
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This § is devoted to the illustration of a “general principle”, which can be stated roughly as follows:
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Central Simple Algebras and Galois Cohomology
2006The first comprehensive, modern introduction to the theory of central simple algebras over arbitrary fields, this book starts from the basics and reaches such advanced results as the Merkurjev–Suslin theorem, a culmination of work initiated by Brauer, Noether, Hasse and Albert, and the starting point of current research in motivic cohomology theory by ...
Philippe Gille, Tamás Szamuely
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Galois cohomology of the classical groups over fields of cohomological dimension?2
Inventiones Mathematicae, 1995E Bayer-Fluckiger +2 more
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