Jump to ContentJump to Main Navigation
Arithmetic Compactifications of PEL-Type Shimura Varieties$
Users without a subscription are not able to see the full content.

Kai-Wen Lan

Print publication date: 2013

Print ISBN-13: 9780691156545

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691156545.001.0001

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2022. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 30 June 2022

Algebraic Constructions of Toroidal Compactifications

Algebraic Constructions of Toroidal Compactifications

(p.373) Chapter Six Algebraic Constructions of Toroidal Compactifications
Arithmetic Compactifications of PEL-Type Shimura Varieties

Kai-Wen Lan

Princeton University Press

This chapter explains the algebraic construction of toroidal compactifications. For this purpose the chapter utilizes the theory of toroidal embeddings for torsors under groups of multiplicative type. Based on this theory, the chapter begins the general construction of local charts on which degeneration data for PEL structures are tautologically associated. The next important step is the description of good formal models, and good algebraic models approximating them. The correct formulation of necessary properties and the actual construction of these good algebraic models are the key to the gluing process in the étale topology. In particular, this includes the comparison of local structures using certain Kodaira–Spencer morphisms. As a result of gluing, this chapter obtains the arithmetic toroidal compactifications in the category of algebraic stacks. The chapter is concluded by a study of Hecke actions on towers of arithmetic toroidal compactifications.

Keywords:   toroidal compactifications, toroidal embeddings, good algebraic models, étale topology, Kodaira–Spencer morphisms, algebraic stacks, Hecke actions, arithmetic toroidal compactifications

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.