##
Seminar on Honda-Tate theory and applications (Spring 2023)

The plan is to go through the proof of:

Theorem (Honda-Tate): Isogeny classes of abelian varieties over the finite field with q elements are in bijection with q-Weil polynomials.

The bijection is given by the Honda-Tate map that sends an abelian variety to the characteristic polynomial of its Frobenius endomorphism.

The talks will given mostly by students and postdocs. Our main reference is §16 of *Abelian Varieties* by Edixhoven, Moonen, and van der Geer.

April 16 (Ari): Intro/motivation

April 30 + May 7 (David Lilienfeldt): Positivity of Rosati involution and defining the Honda-Tate map

May 14 (Arieh Zimmerman): Tate's theorem and injectivity of the Honda-Tate map.

May 21 (Georgios Papas): Corollaries of Tate's theorem
May 28 (Asaf Yekutieli): Abelian varieties with complex multiplication and surjectivity of the Honda-Tate map
June 4 (?): Finishing up proof
June 11-? (?): Applications