organized by Zeyu Shen.

Topic: abelian varieties

references:

abelian varieties notes by Bas Edixhoven, Gerard van der Geer, Ben Moonen.

abelian varieties notes by James Milne in Arithmetic Geometry edited by Gary Cornell and Joseph H. Silverman.

May 22nd: talk by Zengrui Han, definition of abelian varieties, group varieties are smooth, the tangent bundle of a group variety is trivial.

May 25th: talk by Zengrui Han, group of rational points on an elliptic curve isomorphic to the kernel of the degree homomorphism, elliptic curves are 1-dimensional abelian varieties.

May 29th: talk by Zengrui Han, rigidity theorem, morphism of abelian varieties is composition of a homomorphism and a right translation.

June 5th: talk by Zeyu Shen, an invertible sheaf on a complete variety is trivial if and only if both the sheaf and its dual have nonzero global sections, proof of the seesaw principle.

June 8th: talk by Zeyu Shen, proof of theorems of the cube and the square.

June 12th: talk by Zeyu Shen, abelian varieties are projective, every abelian variety has a symmetric ample invertible sheaf.

June 15th: talk by Zengrui Han, functorial characterization of group schemes and subgroup schemes, basic properties of group schemes.

June 19th: talk by Zengrui Han, properties of group schemes locally of finite type over a field.

June 22nd: talk by Zengrui Han, Cartier duality for group schemes.

June 26th: talk by Zeyu Shen, characterization of isogeny for abelian varieties, degree of isogeny.

June 29th: talk by Zeyu Shen, characterizations and examples of separable and purely inseparable isogenies of abelian varieties, group of rational points of an abelian variety over an algebraically closed field is divisible.

July 3rd: talk by Zeyu Shen, relative Frobenius morphism for an abelian variety X over a field of characteristic p is a purely inseparable isogeny of degree p^dim(X).

Jul 6th: talk by Zeyu Shen, dual abelian variety and Poincaré bundle.