Central simple algebras of index p^n in characteristic p
Mathieu Florence (Jussieu)
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When 
Jan 26, 2012 from 03:15 pm to 04:15 pm 
Where  Mainz, 05432 (Hilbertraum) 
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Abstract: Let k be a field of characteristic p>0. In this talk, we shall study palgebras; that is, central simple kalgebras of degree a power of p. By a theorem of Teichmüller, every such algebra (say of exponent e and index d) is Brauer equivalent to a tensor product of cyclic algebras of degree e. Teichmüller moreover proved in the 30's that the number of cyclic algebras appearing in the tensor product can be bounded by d!(d!1) (twenty years ago, this result was improved by Mammone and MammoneMerkurjev in some particular cases). We shall improve this bound down to d1. Key tools are a careful study of the Frobenius morphism for SeveriBrauer varieties, as well as a structure theorem for some commutative unipotent group schemes.