Arithmetic Compactifications of PEL-Type Shimura Varieties
Princeton University Press (Verlag)
978-0-691-15654-5 (ISBN)
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).
Kai-Wen Lan is assistant professor of mathematics at the University of Minnesota.
*FrontMatter, pg. i*Contents, pg. v*Acknowledgments, pg. xi*Introduction, pg. xiii*Chapter One. Definition of Moduli Problems, pg. 1*Chapter Two. Representability of Moduli Problems, pg. 91*Chapter Three. Structures of Semi-Abelian Schemes, pg. 143*Chapter Four. Theory of Degeneration for Polarized Abelian Schemes, pg. 175*Chapter Five. Degeneration Data for Additional Structures, pg. 285*Chapter Six. Algebraic Constructions of Toroidal Compactifications, pg. 373*Chapter Seven. Algebraic Constructions of Minimal Compactifications, pg. 447*Appendix A. Algebraic Spaces and Algebraic Stacks, pg. 487*Appendix B. Deformations and Artin's Criterion, pg. 519*Bibliography, pg. 535*Index, pg. 545
Erscheint lt. Verlag | 24.3.2013 |
---|---|
Reihe/Serie | London Mathematical Society Monographs |
Verlagsort | New Jersey |
Sprache | englisch |
Maße | 178 x 254 mm |
Gewicht | 1134 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
ISBN-10 | 0-691-15654-9 / 0691156549 |
ISBN-13 | 978-0-691-15654-5 / 9780691156545 |
Zustand | Neuware |
Haben Sie eine Frage zum Produkt? |
aus dem Bereich