Perfectoid covers of abelian varieties

Abstract

For an abeloid variety A over an algebraically closed non-archimedean field of residue characteristic p, we show that there exists a perfectoid space which is the tilde-limit of lim ← −[p] A. Our proof also works for the larger class of abeloid varieties. 1 Introduction 631 2 Tilde-limits of rigid groups 635 3 Perfectoid tilde-limits of Raynaud extensions 641 4 The case of abeloid varieties 646 5 Applications 652 References 660