Arithmetic Compactifications of PEL-Type Shimura Varieties
Regular price
€233.12
14 days return policy
Shipping & Delivery
A01=Kai-Wen Lan
Abelian variety
Age Group_Uncategorized
Age Group_Uncategorized
Algebra over a field
Algebraic closure
Algebraic geometry
Algebraic group
Algebraic number field
Algebraic space
Algebraic theory
Arithmetic
Author_Kai-Wen Lan
automatic-update
Automorphic form
Automorphism
Category1=Non-Fiction
Category=PBK
Category=PBM
Category=PBMW
Category=PBP
Cohomology
Commutative property
Compactification (mathematics)
COP=United States
Dedekind domain
Degeneracy (mathematics)
Delivery_Delivery within 10-20 working days
Diagram (category theory)
Dimension (vector space)
Discrete mathematics
Discrete valuation ring
Division algebra
Endomorphism
eq_isMigrated=2
eq_nobargain
Equivalence class
Field of fractions
Finite morphism
Fourier series
Geometric invariant theory
Group scheme
Groupoid
Hermitian symmetric space
Hilbert scheme
Homomorphism
Hopf algebra
Ideal (ring theory)
Invertible sheaf
Isogeny
Isomorphism class
Language_English
Lie algebra
Mathematics
Modular curve
Module (mathematics)
Moduli space
Morphism
Neighbourhood (mathematics)
PA=Available
Polynomial
Presheaf (category theory)
Price_€100 and above
Projective module
Projective variety
PS=Active
Pullback (category theory)
Pullback (differential geometry)
Quasi-projective variety
Residue field
Resolution of singularities
Riemann surface
Ring (mathematics)
Ring homomorphism
Semisimple algebra
Separable algebra
Sheaf (mathematics)
Shimura variety
Sigma-algebra
Simple algebra
softlaunch
Subgroup
Surjective function
Theorem
Topology
Torsor (algebraic geometry)
Valuation ring
Zariski topology
Zariski's main theorem
Product details
- ISBN 9780691156545
- Weight: 1134g
- Dimensions: 178 x 254mm
- Publication Date: 24 Mar 2013
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Hardback
- Language: English
Secure
checkout
Fast Shipping
Easy returns
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).
Kai-Wen Lan is assistant professor of mathematics at the University of Minnesota.
