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#### Arithmetic Compactifications of PEL-Type Shimura Varieties

Princeton University Press 2013; US$ 150.00By 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... more...

#### The Gross-Zagier Formula on Shimura Curves

Princeton University Press 2012; US$ 75.00This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and Swinnerton-Dyer conjecture and Diophantine equations. The book begins with a conceptual formulation... more...

#### On the Cohomology of Certain Non-Compact Shimura Varieties (AM-173)

Princeton University Press 2010; US$ 52.50This 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 intersection cohomology of the Shimura variety associated to a reductive group G carries commuting actions of the absolute Galois group of the reflex field and of the group G(Af) of... more...

#### Applied Algebraic Dynamics

De Gruyter 2009; US$ 196.00This monograph presents recent developments of the theory of algebraic dynamical systems and their applications to computer sciences, cryptography, cognitive sciences, psychology, image analysis, and numerical simulations. The most important mathematical results presented in this book are in the fields of ergodicity, p-adic numbers, and noncommutative... more...

#### The Large Sieve and its Applications

Cambridge University Press 2008; US$ 100.00Explains new applications of the 'large sieve', an important tool of analytic number theory, presenting potential uses beyond this area. more...

#### Logarithmic Forms and Diophantine Geometry

Cambridge University Press 2008; US$ 92.00An account of effective methods in transcendental number theory and Diophantine geometry by eminent authors. more...

#### Heights in Diophantine Geometry

Cambridge University Press 2006; US$ 72.00This monograph is a bridge between the classical theory and modern approach via arithmetic geometry. more...

#### Galois Representations in Arithmetic Algebraic Geometry

Cambridge University Press 1998; US$ 104.00Conference proceedings based on the 1996 LMS Durham Symposium 'Galois representations in arithmetic algebraic geometry'. more...

#### Lectures on Arakelov Geometry

Cambridge University Press 1992; US$ 48.00An account for graduate students of this new technique in diophantine geometry; includes account of higher dimensional theory. more...

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