Reduction of abelian varieties with complex multiplication and its first truncated Barsotti-Tate group schemes (Part II)
Speaker: Dr Alexey Zaytsev (Sch. Math Sc., UCD)
Date: Mon 18th 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 OK 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 pOK into prime ideals and the decomposition of the first truncated Barsotti-Tate group scheme (AmodS)[p].
In the second part of the talk, I will explain the classification of BT_1-group schemes from abelian varieties of dimension 1,2 and 3. Using this classification I will show a correspondence between the decomposition of the ideal pOk and the A[p] as an abelian group scheme over algebraic closure of Fp.
(This talk is part of the Algebra/Claude Shannon Institute series.)