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Oberseminar WiSe 2009/10 Zusammenfassung des Vortrags von I. Dan-Cohen (UC Berkeley, USA)

Moduli of unipotent representations in characteristic 0

Let G be a unipotent group over a field of characteristic zero. From the point of view of moduli, automorphisms of representations of G are badly behaved: they are positive dimensional, and their dimensions can jump in families. An attempt to control the automorphisms leads to the introduction of a certain nondegeneracy condition on representations, as well as an invariant, w, of G, which I call the "width". For n arbitrary, there's an algebraic space parametrizing nondegenerate representations of dimension n, and a concrete construction shows that for n not larger than w +1, this algebraic space is in fact a quasi-projective variety. I hope to convince the audience that both the width and the quasi-projective variety to which it gives rise are natural and interesting objects, worthy of further study.