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Séminaire de Théorie des Nombres

A Galois descent for inseparable field extensions..

Giulia Battiston

( Heidelberg )

Salle de Conférences

le 11 janvier 2019 à 14:00

Let L/K be a Galois separable field extension, then classical Galois descent theory describes algebraic objects over K, such as for example K-varieties, as being equivalent to algebraic objects over L endowed with a Gal(L/K)Gal(L/K)-action which is σ\sigma-linear. If L/K is not separable, though, such a theory does not apply for the simple reason that the field of Gal(L/K)Gal(L/K)-invariants is strictly bigger than K. We will present how this inconvenient can be bypassed using the automorphism group of truncated polynomials over L and hence obtaining a Galois descent theory for inseparable extensions.