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Mathematics Colloquium


Date:  Tuesday, September 20, 2011

Title:  On Division Algebras Having the Same Maximal Subfields

Abstract:  The talk will be built around the following question: let $D_1$ and $D_2$ be two central quaternion division algebras over the same field $K$; when does the fact that $D_1$ and $D_2$ have the same maximal subfields imply that $D_1$ and $D_2$ are actually isomorphic over $K$? I will discuss the motivation for this question that comes from the joint work with G.~Prasad on length-commensurable locally symmetric spaces, and will then talk about some available results. One of the results states that if the answer to the above question is positive over a field $K$ (of characteristic not 2) then it is also positive over any finitely generated purely transcendental extension of $K$. I will also discuss some generalizations to algebras of degree $> 2$ and some recent finiteness results. This is a joint work with V.Chernousov and I.Rapinchuk.

Speaker:  Andrei Rapinchuk
Institution:  University of Virginia


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