Speaker: Zhiyu Zhang

Title: p-divisible groups over O_c

Abstract: It’s known by Riemann that complex tori are classified by lattices in complex vector spaces, which can be reformulated using Hodge structures. A useful application is complex uniformisation of moduli of some abelian varieties. In the  p-adic world, analogous objects are  -divisible groups over O_c (as formal schemes), which are examples of " p-adic Hodge structures”. We will present many evidences with main focus on Scholze-Weinstein’s classification. For the proof, the key guiding example is G= \mu_p\infty  (note \mu_p\infty(O_c)\neq  \lim_{n\to} \mu_p\infty(O_c)/p^n . For simplicity, some technical difficulties will be ignored, e.g the use of adic spaces. Then we will present the Dieudonne theory over O_c /p  , and use it to explain more analogies, e.g every height 2 dimension  1p-divisible group over O_c is from an elliptic curve over  O_c. If time permits, we may explain why the viewpoint of " p-adic Hodge structures” gives the relation of  p-divisible group over O_c   with modification of vector bundles on the Fargues-Fontaine curve.    

The talk will be accompanied by breakfast.