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What Determines an Algebraic Variety?
A pioneering new nonlinear approach to a fundamental question in algebraic geometryOne of the crowning achievements of nineteenth-century mathematics was the proof that the …
On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (AM-157)
In recent years, considerable progress has been made in studying algebraic cycles using infinitesimal methods. These methods have usually been applied to Hodge-theoretic …
Abelian Varieties with Complex Multiplication and Modular Functions
Reciprocity laws of various kinds play a central role in number theory. In the easiest case, one obtains a transparent formulation by means of roots of unity, which are special …
Arithmetic Compactifications of PEL-Type Shimura Varieties
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, …
Lectures on Complex Analytic Varieties (MN-14), Volume 14
This book is a sequel to Lectures on Complex Analytic Varieties: The Local Paranwtrization Theorem (Mathematical Notes 10, 1970). Its unifying theme is the study of local …
Introduction to Toric Varieties. (AM-131), Volume 131
Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. …
Geometry and Cohomology of Some Simple Shimura Varieties. (AM-151), Volume 151
This book aims first to prove the local Langlands conjecture for GLn over a p-adic field and, second, to identify the action of the decomposition group at a prime of bad reduction …
On the Cohomology of Certain Non-Compact Shimura Varieties (AM-173)
This book studies the intersection cohomology of the Shimura varieties associated to unitary groups of any rank over Q. In general, these varieties are not compact. The …