Arithmetic Compactifications of PEL-Type Shimura Varieties

Princeton University Press
Free sample

By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, providing the logical foundation for several exciting recent developments. The book is designed to be accessible to graduate students who have an understanding of schemes and abelian varieties.

PEL-type Shimura varieties, which are natural generalizations of modular curves, are useful for studying the arithmetic properties of automorphic forms and automorphic representations, and they have played important roles in the development of the Langlands program. As with modular curves, it is desirable to have integral models of compactifications of PEL-type Shimura varieties that can be described in sufficient detail near the boundary. This book explains in detail the following topics about PEL-type Shimura varieties and their compactifications:

  • A construction of smooth integral models of PEL-type Shimura varieties by defining and representing moduli problems of abelian schemes with PEL structures
  • An analysis of the degeneration of abelian varieties with PEL structures into semiabelian schemes, over noetherian normal complete adic base rings
  • A construction of toroidal and minimal compactifications of smooth integral models of PEL-type Shimura varieties, with detailed descriptions of their structure near the boundary

Through these topics, the book generalizes the theory of degenerations of polarized abelian varieties and the application of that theory to the construction of toroidal and minimal compactifications of Siegel moduli schemes over the integers (as developed by Mumford, Faltings, and Chai).

Read more

About the author

Kai-Wen Lan is assistant professor of mathematics at the University of Minnesota.
Read more

Reviews

Loading...

Additional Information

Publisher
Princeton University Press
Read more
Published on
Mar 21, 2013
Read more
Pages
584
Read more
ISBN
9781400846016
Read more
Read more
Best For
Read more
Language
English
Read more
Genres
Mathematics / Calculus
Mathematics / Geometry / Algebraic
Mathematics / Geometry / General
Mathematics / Mathematical Analysis
Mathematics / Topology
Read more
Content Protection
This content is DRM protected.
Read more
Eligible for Family Library

Reading information

Smartphones and Tablets

Install the Google Play Books app for Android and iPad/iPhone. It syncs automatically with your account and allows you to read online or offline wherever you are.

Laptops and Computers

You can read books purchased on Google Play using your computer's web browser.

eReaders and other devices

To read on e-ink devices like the Sony eReader or Barnes & Noble Nook, you'll need to download a file and transfer it to your device. Please follow the detailed Help center instructions to transfer the files to supported eReaders.
Mark Ryan
©2017 GoogleSite Terms of ServicePrivacyDevelopersArtistsAbout Google
By purchasing this item, you are transacting with Google Payments and agreeing to the Google Payments Terms of Service and Privacy Notice.