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An analog of a theorem of Lange and Stuhler for principal bundles by Indranil Biswas; Laurent Ducrohet is a Mathematics article available to read on EtoBox.

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Let k be an algebraically closed field of characteristic p > 0 and G the base change to k of a connected reduced linear algebraic group defined over Z/pZ. Let E G be a principal G-bundle over a projective variety X defined over the field k. Assume that there is an étale Galois covering f : Y → X with degree(f ) coprime to p such that the pulled back principal G-bundle f \* E G is trivializable. Then there is a positive integer n such that the pullback This can be considered as a weak converse of the following observation due to P. Deligne. Let H be any algebraic group defined over k and E H a principal H -bundle over a scheme Z. If the pulled back principal H -bundle (F n Z ) \* E H over Z is isomorphic to E H for some n > 0, where F Z is the absolute Frobenius morphism of Z, then there is a finite étale Galois cover of Z such that the pullback of E H to it is trivializable.

Who reads An analog of a theorem of Lange and Stuhler for principal bundles?

Author

Indranil Biswas; Laurent Ducrohet

Publisher

Elsevier Science; Elsevier ; Elsevier Masson; Elsevier BV; Cellule MathDoc/CEDRAM (ISSN 1631-073X)

Published

2007

Field

Mathematics (Physical Sciences)