Reduction of abelian varieties with complex multiplication and its first truncated Barsotti-Tate group schemes
Speaker: Dr Alexey Zaytsev (Sch. Math Sc., UCD)
Date: Mon 4th April 2011
Location: Mathematical Sciences Seminar Room
Let A be an abelian variety over a number field L with complex multiplication by the full ring of integers O_K for some CM field K. We consider a good reduction at prime ideal S in L of the abelian variety A. After the reduction we get an abelian variety over a finite field of characteristic p. In this talk I explain a correspondence between the decomposition of the ideal pO_K into prime ideals and the decomposition of the first truncated Barsotti-Tate group scheme (A mod S)[p].
(This talk is part of the Algebra/Claude Shannon Institute series.)