Results 1 to 10 of about 6,169 (67)

Hopf Galois theory of separable field extensions [PDF]

, 2016
Hopf Galois theory is a generalization of Galois theory. Galois theory gives a bijective correspondence between intermediate fields of a Galois field extension (normal and separable) and subgroups of the Galois group. Hopf Galois theory substitutes the Galois group by a Hopf algebra.
Salguero Garcı́a, Marta
openaire   +2 more sources

Hopf Galois theory for separable field extensions

Journal of Algebra, 1987
The concept of an extension \(S\supseteq R\) of commutative rings being an \(H\)-Galois extension for some Hopf \(R\)-algebra \(H\) has been available since the work of \textit{S. U. Chase} and \textit{M. E. Sweedler} [Hopf algebras and Galois theory. Lect. Notes Math. 97.
Pareigis, Bodo, Greither, C.
openaire   +3 more sources

PAC Fields over Finitely Generated Fields [PDF]

, 2007
We prove the following theorem for a finitely generated field $K$: Let $M$ be a Galois extension of $K$ which is not separably closed. Then $M$ is not PAC over $K$.Comment: 7 pages, Math.
Ben Omrane, Ines, Gala, Sadek, Kim, Jae-Myoung, Ragusa, Maria Alessandra   +3 more
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From Galois to Hopf Galois: theory and practice

, 2014
Hopf Galois theory expands the classical Galois theory by considering the Galois property in terms of the action of the group algebra k[G] on K/k and then replacing it by the action of a Hopf algebra.
Crespo, Teresa, Rio, Anna, Vela, Montserrat   +2 more
core   +1 more source

Galois covers of the open p-adic disc

, 2011
This paper investigates Galois branched covers of the open $p$-adic disc and their reductions to characteristic $p$. Using the field of norms functor of Fontaine and Wintenberger, we show that the special fiber of a Galois cover is determined by ...
B. Green, B. Green, F. Oort, I. Bouw, J. Bertin, J. Lubin, J. Neukirch, J.P. Wintenberger, M. Garuti, Scott Corry, T. Chinburg   +10 more
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Totaro's question for G_2, F_4, and E_6

, 2004
In a 2004 paper, Totaro asked whether a G-torsor X that has a zero-cycle of degree d > 0 will necessarily have a closed etale point of degree dividing d, where G is a connected algebraic group.
Garibaldi, Skip, Hoffmann, Detlev
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A Birational Anabelian Reconstruction Theorem for Curves over Algebraically Closed Fields in Arbitrary Characteristic

, 2018
The aim of Bogomolov's programme is to prove birational anabelian conjectures for function fields $K|k$ of varieties of dimension $\geq 2$ over algebraically closed fields. The present article is concerned with the 1-dimensional case.
Lüdtke, Martin
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The Semisimplicity Conjecture for A-Motives

, 2008
We prove the semisimplicity conjecture for A-motives over finitely generated fields K. This conjecture states that the rational Tate modules V_p(M) of a semisimple A-motive M are semisimple as representations of the absolute Galois group of K.
Bourbaki, Jacobson, Nicolas Stalder, Taguchi, Tamagawa, Tamagawa   +5 more
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Endomorphisms of abelian varieties, cyclotomic extensions and Lie algebras

, 2010
We prove an analogue of the Tate conjecture on homomorphisms of abelian varieties over infinite cyclotomic extensions of finitely generated fields of characteristic zero.Comment: 9 ...
Ch. W. Curtis, D. Mumford, F. A. Bogomolov, F. A. Bogomolov, F. A. Bogomolov, G. Faltings, J. T. Tate, J.-P. Serre, J.-P. Serre, J.-P. Serre, J.-P. Serre, J.-P. Serre, J.-P. Serre, J.-P. Serre, J.-P. Serre, J.-P. Serre, R. Noot, Yu. G. Zarhin, Yu. G. Zarkhin (Zarhin), Yurii G Zarhin   +19 more
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Homogeneous spaces, algebraic $K$-theory and cohomological dimension of fields

, 2019
Let $q$ be a non-negative integer. We prove that a perfect field $K$ has cohomological dimension at most $q+1$ if, and only if, for any finite extension $L$ of $K$ and for any homogeneous space $Z$ under a smooth linear connected algebraic group over $L$,
Arteche, Giancarlo Lucchini, Izquierdo, Diego   +1 more
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