Abelian varieties over finite fields

Abstract

The Lenstra Treurfeest — A farewell conference, in honor of Hendrik W. Lenstra jr Berkeley, 21/22/23 - III - 2003 Some ideas, principles of thought and proof:

• Study abelian varieties over finite fields, but also abelian varieties varying in a family number theory ´and geometry. • A well-know technique in algebraic geometry: study structures by degenerations. For abelian varieties in characteristic p we do not degenerate the abelian variety, but specialize the p-structure, “go to the boundary”, and draw conclusions for the starting position. • Supersingular abelian varieties show a totally different behavior in contrast with nonsupersingular abelian varieties.