eTextbook: Arithmetic Compactifications of PEL-Type Shimura Varieties

Book Jacket Image

List Price 1: $300.00

eTextbook Purchase: $120.00

You save $180.00

Are you a school looking to buy multiple copies of this book?

  • Free Book Promotion

    For a limited time, this book is eligible for free.

    Click here to redeem the Facebook Offer

    Author(s): Lan, Kai-Wen

    ISBN 10: 0691156549. See all ISBN's

    ISBN 13: 9780691156545

    Edition:

    Publisher: Princeton University Press

    This is an eTextbook Learn More

    Description:

    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).

    All ISBN's for this title:

    ISBN 10: 0691156549, ISBN 13: 9780691156545, eISBN 10: 1400846013, eISBN 13: 9781400846016

    1. List price can refer to either the digital or print list price, whichever is available to Kno.
  • Cool Product Features

    Kno In Action

    Search

    Journal

    Flashcards

    Kno Me

    Smart Links