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Galois Seminar

Friday, February 16, 2018 - 3:15pm

Andrei Rapinchuk

University of Virginia


University of Pennsylvania

DRL 4N30

Let D be a central division algebra of degree n over a field
K. One defines the genus gen(D) of D as the set of classes [D'] in the
Brauer group Br(K) where D' is a central division K-algebra of degree n
having the same isomorphism classes of maximal subfields as D. I will review
the results on gen(D) obtained in the last several years, in particular the
finiteness theorem for gen(D) when K is finitely generated of characteristic
not dividing n. I will then discuss how the notion of genus can be extended
to arbitrary absolutely almost simple algebraic K-groups using maximal
K-tori in place of maximal subfields, and report on some recent progress in
this direction. (Joint work with V. Chernousov and I. Rapinchuk)