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Arithmetical algebraic geometry
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  • Heights in Diophantine Geometryby Enrico Bombieri; Walter Gubler; Bela Bollobas; William Fulton; Anatole Katok; Frances Kirwan; Peter Sarnak; Barry Simon

    Cambridge University Press 2006; US$ 78.00

    Diophantine geometry has been studied by number theorists for thousands of years, this monograph is a bridge between the classical theory and modern approach via arithmetic geometry. The treatment is largely self-contained, with proofs given in full detail. Many results appear here for the first time. more...

  • Logarithmic Forms and Diophantine Geometryby A. Baker; G. Wüstholz

    Cambridge University Press 2008; US$ 68.00

    An account of effective methods in transcendental number theory and Diophantine geometry by eminent authors. more...

  • The Large Sieve and its Applicationsby Emmanuel Kowalski

    Cambridge University Press 2008; US$ 85.00

    Explains new applications of the 'large sieve', an important tool of analytic number theory, presenting potential uses beyond this area. more...

  • Applied Algebraic Dynamicsby Vladimir Anashin; Andrei Khrennikov

    Walter de Gruyter, Inc. 2009; US$ 140.00

    This 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 groups. For students and researchers working on the theory of dynamical systems, algebra, number theory, measure theory, computer sciences, cryptography, and image analysis. more...

  • On the Cohomology of Certain Non-Compact Shimura Varieties (AM-173)by Sophie Morel

    Princeton University Press 2010; US$ 45.00

    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 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 finite adelic points of G. The second action can be studied on the set of complex points of the Shimura variety. In this book, Sophie Morel identifies the Galois action--at good places--on the G(Af)-isotypical components of the cohomology. Morel uses the method developed by Langlands, Ihara, and Kottwitz, which is to compare the Grothendieck-Lefschetz fixed point formula and the Arthur-Selberg... more...

  • Lectures on Arakelov Geometryby C. Soulé; D. Abramovich; J. F. Burnol; J. K. Kramer

    Cambridge University Press 1992; US$ 37.00

    An account for graduate students of this new technique in diophantine geometry; includes account of higher dimensional theory. more...

  • Galois Representations in Arithmetic Algebraic Geometryby A. J. Scholl; R. L. Taylor

    Cambridge University Press 1998; US$ 88.00

    Conference proceedings based on the 1996 LMS Durham Symposium 'Galois representations in arithmetic algebraic geometry'. more...

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