Arithmetic Compactifications of Pel Type Shimura Varieties - Couverture rigide

Lan, Kai-Wen

 
9780691156545: Arithmetic Compactifications of Pel Type Shimura Varieties
Couverture rigide
ISBN 10 : 0691156549 ISBN 13 : 9780691156545
Editeur : Princeton University Press, 2013

Synopsis

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).

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l?auteur

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

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Princeton University Press
Date d'édition
2013
Langue
anglais
ISBN 10 
0691156549
ISBN 13 
9780691156545
Reliure
Relié
Nombre de pages
584
Coordonnées du fabricant
non disponible
Personne responsable
non disponible