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