Dr Alexey Zaytsev (Sch. Math Sc., UCD)

will speak on

Reduction of abelian varieties with complex multiplication and its first truncated Barsotti-Tate group schemes (Part II)

Time: 4:00PM
Date: Mon 18th April 2011
Location: Mathematical Sciences Seminar Room [map]

Further information

Abstract: 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 $(A {\rm mod} S)[p]$.

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 $pO_k$ and the $A[p]$ as an abelian group scheme over algebraic closure of $F_p$.

(This talk is part of the Algebra and Number Theory series.)

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