MATH Seminar

Title: On division algebras having the same maximal subfields
Seminar: Algebra and number theory
Speaker: Andrei Rapinchuk of University of Virginia
Contact: R. Parimala, parimala@mathcs.emory.edu
Date: 2011-02-08 at 3:00PM
Venue: W306
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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 (joint with I.~Rapinchuk) 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 $> 2$.