Introduction padic symmetric domains quasiisogenies of pdivisible groups moduli spaces of pdivisible groups appendix. Request pdf on period spaces for pdivisible groups in their book rapoport and zink constructed rigid analytic period spaces for fontaines. We show how to characterize integral models of shimura varieties over places of the reflex field where the level subgroup is tame parahoric by formulating a definition of a canonical integral model. Pdf document information annals of mathematics fine hall washington road princeton university princeton, nj 08544, usa phone. Zink, purity results for pdivisible groups and abelian schemes over regular bases of mixed characteristic. It is fully faithful, if the ideal of nilpotent elements in ris a nilpotent ideal. Zink, breuils classification of pdivisible groups over regular local rings of arbitrary dimension.
Period spaces for pdivisible groups am141, volume 141 by michael rapoport. The padic uniformization of shimura varieties 273 bibliography 317 index 323. International press of boston publishers of scholarly mathematical and scientific journals and books. April 25, 2008 abstract in their book rapoport and zink constructed rigid analytic period spaces for fontaines. We can study variants of pdivisible groups that have additional structure e. These were studied extensively by morita, orlik, schneider. Along the way, we discuss many foundational topics in the padic theory of abelian varieties, p. Subgroups of pdivisible groups and centralizers in. The restriction of the functor bt to the category of displays is faithful. This write up is devoted to some basic but important aspects of the structure theory of pdivisible groups. Discussion session on pdivisible groups notes by tony feng april 7, 2016 these are notes from a discussion session of pdivisible groups. A morphism between pdivisible groups is a collection of morphisms f.
Using the concept of rigidanalytic period maps the relation of padic period domains to moduli space of pdivisible groups is investigated. A pdivisible group g over r of height h is an inductive system g g. In this monograph padic period domains are associated to arbitrary reductive groups. We consider the newton polygon stratification of the special fiber at p of shimura varieties and show that each newton polygon stratum can be described in terms of the products of the reduced fibers of the corresponding peltype. There is a deep correspondence between the morava etheory of spaces and the algebraic geometry of the formal group associated to e n.
In their book rapoport and zink constructed rigid analytic period spaces for fontaines filtered isocrystals, and period morphisms from moduli spaces of pdivisible groups to some of these period spaces. The following main theorem gives the comparison of our theory and the crystalline dieudonn e theory of grothendieck and messing. The period morphism and the rigidanalytic coverings. Divisible groups are important in understanding the structure of abelian groups, especially because they are the injective abelian. Our main goal is to prove that rapoportzink spaces at infinite level are naturally perfectoid spaces, and to give a description of these spaces purely in terms of padic hodge theory.
Hecke orbits, and the grothendieck conjecture in this section we discuss the two theorems we are going to consider. On period spaces for pdivisible groups request pdf. Using the concept of rigidanalytic period maps the relation of p adic period domains to moduli space of p divisible groups is investigated. In this monographpadic period domains are associated to arbitrary reductive groups.
In this paper we compute the e ect of the transchromatic. Using the concept of rigidanalytic period maps the relation ofpadic period domains to moduli space ofpdivisible groups is investigated. Some questions were posed by dennis gaitsgory, and then their answers were discussed by jared weinstein. We determine the image of these period morphisms, thereby contributing to. Inverse limits in the category of adic spaces 19 3. In mathematics, especially in the field of group theory, a divisible group is an abelian group in which every element can, in some sense, be divided by positive integers, or more accurately, every element is an nth multiple for each positive integer n. Review of the first three sections of rapoportzink 96 is inrapoportzink spaces, lecture notes 20 pdf. In their book rapoport and zink constructed rigid analytic period spaces for fontaines. These period spaces are analogs of the rapoportzink period spaces for fontaines filtered isocrystals in mixed characteristic and likewise are rigid analytic spaces. Hoaran wang, moduli spaces of pdivisible groups and period morphisms, masters thesis, 2009, pdf. Moduli spaces of pdivisible groups and period morphisms.
We determine the image of these period morphisms, thereby contributing to a question of grothendieck. The space of level 0, and the period morphism 44 6. Rapoport, michael zink, thomas period spaces for pdivisible groups am141, volume 141. We determine the image of these period morphisms, thereby answering a question of grothendieck. Iwasawa modules arising from deformation spaces of p. In their book period spaces for pdivisible groups, rapoport and zink construct the rigid analytic period spaces for. Period spaces for hodge structures in equal characteristic. The universal vector extension, and the universal cover 24 3.
Volume 346, issues 2122 pages 11231218 november 2008 download full issue. We determine the image of these period morphisms, thereby answering a. For our period spaces we prove the analog of a conjecture of rapoport and zink stating the existence of a universal local system on a berkovich open subspace of the period. Available formats pdf please select a format to send.
Period spaces for pdivisible groups am141, volume 141. Pis a formal pdivisible group of height equal to rank rp. Save up to 80% by choosing the etextbook option for isbn. Tate 1967 defined a pdivisible group of height h over a scheme s to be an inductive system of groups g n for n. Historically, results and conjectures surrounding pdivisible groups were the main stimulus for the development of padic hodge theory, and they continue to be relevant in modern research. K on the completion c of the algebraic closure of a local field k of characteristic 0. Iwasawa modules arising from deformation spaces of pdivisible formal group laws. Our main goal is to prove that rapoportzink spaces at infinite level are naturally perfectoid spaces, and to give a. Algebraic and arithmetic structures of moduli spaces, sapporo japan 2007. Subgroups of pdivisible groups and centralizers in symmetric groups nathaniel stapleton november 8, 20. Zink, period spaces for p pdivisible groups, annals of mathematics studies, vol. In addition, nonarchimedean uniformization theorems for general shimura varieties are established. Thomas zink and publisher princeton university press.
These are necessary in the rapoportzinks construction of period mappings for pdivisible groups. There is a tower of coverings of mrig via level structures on the tate module of the universal pdivisible. Statement of purpose the aim here is simply to provide some details to some of the proofs in tates paper t. Normal forms of lattice chains the formal hecke correspondences the period morphism and the rigidanalytic coverings padic uniformization of shimura varieties.
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