Nov 01, 2008 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. Internal revenue service an official website of the. We determine the image of these period morphisms, thereby answering a question of grothendieck. On the hodgenewton filtration for pdivisible groups with. Fp, the moduli space of polarized abelian varieties of dimension g in positive. Period spaces for pdivisible groups am141, volume 141 details authors. Using the concept of rigidanalytic period maps the relation ofpadic period domains to moduli space ofpdivisible groups is investigated. Jared weinstein, the geometry of lubitate spaces, lecture 1. Moreover, we identify the image of the period morphism, reproving results of. Part ii brandon levin this talk discusses the main results of tates paper pdivisible groups 6. The space m is a formal scheme representing a moduli functor of pdivisible. Subgroups of pdivisible groups and centralizers in. Apr 08, 2018 richard pink, finite group schemes, 20042005, pdf.
One can show that the system also satis es ii making it a pdivisible group, called the serre dual of g. In this monographpadic period domains are associated to arbitrary reductive groups. A classi cation of pdivisible groups over o k 24 6. Minimal pdivisible groups by frans oort introduction a pdivisible group x can be seen as a tower of building blocks, each of which is isomorphic to the same. Thegroup strnctureis described by homomorphisms jl. The global structure of moduli spaces of polarized divisible. 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. The padic uniformization of shimura varieties 273 bibliography 317 index 323. We then construct the period morphism on the rigid generic fibre. Request pdf on period spaces for pdivisible groups in their book rapoport and zink constructed rigid analytic period spaces for fontaines filtered isocrystals, and period morphisms from.
Divisible groups are important in understanding the structure of abelian groups, especially because they are the injective abelian groups. If the inline pdf is not rendering correctly, you can download the pdf file here. Applications to pdivisible groups and finite group schemes. For ordinary abelian groups, these axioms imply that g. Such a g is defined by a locally free sheafofaigebras a ofrankmoverr.
I believe a more streamlined approach to the theory exists due to fontaine, but i have chosen to take the classical approach below. Moduli spaces of pdivisible groups and period morphisms. In their book rapoport and zink constructed rigid analytic period spaces for fontaines filtered isocrystals, and period morphisms from moduli spaces of p divisible groups to some of these period spaces. 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. In the rst part of this subsection, we do not assume that the pdivisible group g lim. We give definitions, properties, examples, and open problems.
The supersingular locus of the shimura variety of gu1, n. We study the global structure of moduli spaces of quasiisogenies of pdivisible groups introduced by rapoport and zink. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Zink princeton university press princeton, new jersey 1996. Some of the descriptions of the talks are a little sketchy, so feel free to ask for. Dieudonne modules free wkmodules with semilinear actions of frobenius and. Find customizable templates, domains, and easytouse tools for any type of business website. The monthly calendar 2021 with 12 months on 12 pages one month per page, us letter paper format, available in ms word doc, docx, pdf and jpg file formats. The multiplication by p on a pdivisible group is obviously an isogeny. We determine the image of these period morphisms, thereby contributing to a question of grothendieck. Share photos and videos, send messages and get updates. A pdivisible group of height hover a scheme sis an inductive system g fg vg. The theory of pdivisible groups plays an important role in arithmetic.
Tate a pdivisible group on s is an inductive system gnn2n of. Moduli of abelian varieties and pdivisible groups penn math. On period spaces for pdivisible groups sciencedirect. This allows us to formulate and prove duality isomorphisms between basic rapoportzink spaces at infinite level in general. Monthly calendar 2021 free download, editable and printable. Connect with friends, family and other people you know. A quasiisogeny of pdivisible groups from g to g0 is a global section of. More precisely, given an isogeny class of barsottitate groups with unramified additional structures, we investigate how the associated nonbasic moduli spaces compare to the basic moduli spaces associated with its isoclinic constituents. Monthly calendar 2021 free download monthly 2021 calendar templates including week numbers, holidays on red and space for notes. Hoaran wang, moduli spaces of pdivisible groups and period morphisms, masters thesis, 2009, pdf. Princeton university press books are printed on acid free paper and meet the guidelines. Introduction let x be a smooth projective algebraic variety over r. The new payment will be larger for most eligible people.
The period morphism and the rigidanalytic coverings. Princeton university press books are printed on acidfree paper and meet the guidelines. Families of pdivisible groups with constant newton polygon. Let x be an abelian variety then xp xp has a natural a structure of pdivisible group of height 2n, where dimx n. Smoothness of the truncated display functor american. Research of rapoport supported by sfbtr 45 periods, moduli spaces and. This is a set of notes for a course we gave in the second week of august in the 2006 cmi summer school at go. Moduli spaces of polarized pdivisible groups 829 for the case of moduli of pdivisible groups for g glh, the analogousformula for the dimension is shown in v1. Thus, te l is a vector space of dimension ndimg over l. The global structure of moduli spaces of polarized.
Adobe acrobat reader dc software is the free global standard for reliably viewing, printing, and commenting on pdf documents. Dec 22, 1995 in this monograph padic period domains are associated to arbitrary reductive groups. Nontrivial divisible groups are not finitely generated. Subgroups of pdivisible groups and centralizers in symmetric. We determine their dimensions and their sets of connected components and of irreducible components. Using the concept of rigidanalytic period maps the relation of padic period domains to moduli space of pdivisible groups is investigated. Each pdivisible group has a dual group induced from the dual diagram of. In this monograph padic period domains are associated to arbitrary reductive groups. Jun 16, 2009 the notions hodgenewton decomposition and hodgenewton filtration for fcrystals are due to katz and generalize messings result on the existence of the localetale filtration for pdivisible groups. Period spaces for pdivisible groups am141, volume 141. In their book rapoport and zink constructed rigid analytic period spaces for fontaines. Mar 02, 2018 in this talk the algebraic object will be a finite group scheme or a pdivisible group and the geometric objects considered are abelian varieties. The exposition includes background material on grothendiecks.
If g is a finite locally free commutative group scheme we write ver verg. 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. In addition, nonarchimedean uniformization theorems for general shimura varieties are established. For 0 n 2 dimx, there is a period pairing hn dr xcr h nxc. X 2pdoes in general not imply that x 1 and x 2 are isomorphic. Explain sketch how the notion of p divisible group is related to the notion of. In this paper we study certain moduli spaces of barsottitate groups constructed by rapoport and zink as local analogues of shimura varieties.
Weebly s free website builder makes it easy to create a website, blog, or online store. To do this, well study the pdivisible group associated to a. And now, its connected to the adobe document cloud. If the isocrystals of the pdivisible groups are simple, we compute the cohomology of the moduli space. This is apparent in theorems such as stricklands work 10 that relates the etheory of symmetric groups modulo a transfer ideal to the scheme classifying. It is a finitely generated free wfcmodule which is equipped with. Letr be a commutativering or a prescheme, by afinite group ofordermoverr we shall meana groupscheme gwhich is locally free of rank mover r. Relative breuilkisin classification of pdivisible groups. Apr 08, 2016 finally, to extend our results to all divisible groups, not just the geometrically connected ones, well have to make extensive use of cartier duality. Serretate equivalence for connected pdivisible groups. We prove several results about moduli spaces of p divisible groups such as.
From the point of view of padic hodge theory, this is a foundational paper and within this setting, much of the. We prove several results about pdivisible groups and rapoportzink spaces. Zink, period spaces for p divisible groups, annals of. Using the concept of rigidanalytic period maps the relation of padic period domains to moduli space of p divisible groups is investigated. It follows that for pdivisible groups, the group hom sg. These methods give rise to geometric structures, when we keep these invariants fixed. We prove that, for a pdivisible group with additional structures over a complete valuation ring of rank 1 o k with mixed characteristic 0,p, if the newton polygon and the hodge polygon of its special fiber possess a nontrivial contact point, which is a break point for the newton polygon, then it admits of a hodgenewton filtration over o k. Pdf on nonbasic rapoportzink spaces semantic scholar. Pel type rapoportzink space deformation space of p divisible groups with. Our main goal is to prove that rapoportzink spaces at infinite level are naturally perfectoid spaces, and to give a. The purpose of this course was to carefully lay the foundations for.
Further, every abelian group can be embedded in a divisible group as an essential subgroup in a unique way. On period spaces for pdivisible groups request pdf. There, the sets of connected components and of irre. April 25, 2008 abstract in their book rapoport and zink constructed rigid analytic period spaces for fontaines. 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. Foxit software is the reliable source for fast, affordable, and secure pdf solutions. Oct 30, 2014 the relative breuilkisin classification of pdivisible groups and finite flat group schemes wansu kim department of pure mathematics and mathematical statistics, university of cambridge, cambridge cb3 0wb, uk. Frontmatter was published in period spaces for pdivisible groups am141, volume 141 on page i. On the drinfeld moduli problem of pdivisible groups mathematical. Although p divisible groups are interesting enough in their own. Moduli of abelian varieties and pdivisible groups chingli chai and frans oort abstract. Every abelian group can be embedded in a divisible group. An abelian group is divisible if and only if it is pdivisible for every prime p. A crystal over k is a free wkmodule m of finite rank.
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