Reading Seminar Summer 2026

This is the homepage for the reading group on isocrystals. The main plan is to introduce the notion for F-isocrystals, compare different categories for isocrystals and prove the parabolicity conjecture of F-isocrystals. We'll mainly follow the notes of Kiran Kedlaya and the paper of Marco D'Addezio.

If time's permitted, we also will cover some applications to the theory of companions, rational points on abelian varieties and other topics.

Weekly Plan:

1. Week one: A review on the theory of (pointwise) F-isocrystals.
2. Week two: The theory of (overconvergent) F-isocrystals.

References:

1. Notes on isocrystals, Kiran Kedlaya.
2. Parabolicity conjecture of F-isocrystals, Marco D'Addezio.
3. F-isocrystals and their monodromy groups, Richard Crew.
4. Parabolicity conjecture of F-isocrystals, Marco D'Addezio.
5. Maximal tori of monodromy groups of F-isocrystals and an application to abelian varieties, Marco D'Addezio and Emiliano Ambrosi.
6. Perfect points of abelian varieties, Emiliano Ambrosi.