# Jakob Stix: Categories of abelian varieties over finite fields

**Time: **
Wed 2022-05-04 13.15

**Location: **
Zoom, meeting ID: 694 6016 6420 (password required)

**Participating: **
Jakob Stix (University Frankfurt am Main)

**Abstract:**

Abelian varieties over finite fields are described up to isogeny by Weil numbers. We will recall this Honda-Tate theory and explain how to raise the description to a categorical level in terms of categories of modules. This extends and reproves prior equivalences of categories by Deligne for ordinary abelian varieties to the case of all abelian varieties over finite fields. A prominent role in the theory is played by what we call locally projective abelian varieties. This is joint work with Tommaso Centeleghe.

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