On certain representations of automorphism groups of an algebraically closed field

Details On certain representations of automorphism groups of an algebraically closed field On certain representations of automorphism groups of an algebraically closed field

2001-01-20

arxiv.org/abs/math/0101170v9

Math. Zeitschrift 249 (2005), no.1, 163--221

Mathematics

Representation Theory

Scientific paper

Let k be an algebraically closed field of characteristic zero, F its algebraically closed extension, and G be the group of k-automorphisms of F endowed with a natural topology. One of the purposes of this paper is to show that any non-faithful continuous representation of G factors through a discrete quotient of G. Properties of representation of G arising from geometry are studied. In some cases the groups of morphisms between geometric objects are identified with the groups of morphisms between corresponding G-modules, and the ${\rm Ext}^1$'s are related. In particular, the category of abelian varieties over k with morphisms tensored with the rationals can be described as a category of G-modules.

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