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Arithmetic and Geometry

Serre's conjecture and on rational points on algebraic varieties. The resulting proceedings volume provides a modern overview of the subject for;

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Geometry of Moduli

differentials, (log) Calabi-Yau varieties, points on schemes, rational varieties, curves, abelian varieties and hyper-Kahler manifolds.;

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Galois Representations in Arithmetic Algebraic Geometry

attention, e.g. Erez on geometric trends in Galois module theory; Mazur on rational points on curves and varieties; Moonen on Shimura varieties;

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Number Theory and Algebraic Geometry

in analytic and arithmetic number theory, and algebraic geometry. The topics treated include: rational points on algebraic varieties, the Hasse;

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Arithmetic of Higher-Dimensional Algebraic Varieties

of higher dimensional varieties. Recently, it has become clear that ideas from many branches of mathematics can be successfully employed in the;

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Cambridge Studies in Advanced Mathematics

The most basic algebraic varieties are the projective spaces, and rational varieties are their closest relatives. In many applications;

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Rigid Cohomology

cohomology. It is a p-adic Weil cohomology suitable for computing Zeta and L-functions for algebraic varieties on finite fields. Moreover, it;

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Integral Points on Algebraic Varieties

points on algebraic varieties. This text rapidly introduces problems in Diophantine Geometry, especially those involving integral points;

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Rational Points on Varieties

This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a;

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Number Theory Related to Modular Curves

of Galois representations attached to modular forms, rational points on elliptic and modular curves, modularity of some families of Abelian;

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London Mathematical Society Lecture Note Series

Ever since the seminal work of Goppa on algebraic-geometry codes, rational points on algebraic curves over finite fields have been an;

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Surveys in Differential Geometry Vol II

This collection of essays on differential geometry includes: the formation of singularities; spaces of algebraic cycles; rational points;

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Sheaves and Functions Modulo P: Lectures on the Woods Hole Trace Formula

of the sheaves-functions dictionary of Deligne, relating characteristic-p-valued functions on the rational points of varieties over finite fields;

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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;

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Cambridge Tracts in Mathematics

The classical descent on curves of genus one can be interpreted as providing conditions on the set of rational points of an algebraic;

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The Gross-Zagier Formula on Shimura Curves

incoherent automorphic representations with rational coefficients attached naturally to abelian varieties parametrized by Shimura curves. This;

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The Gross-Zagier Formula on Shimura Curves

incoherent automorphic representations with rational coefficients attached naturally to abelian varieties parametrized by Shimura curves. This;

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Brauer Groups and Obstruction Problems

applications, the book extends a number of powerful tools for analyzing rational points on elliptic curves, e.g., isogenies among curves, torsion;

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Higher Dimensional Birational Geometry

of abelian surfaces, rational curves on algebraic varieties, 3-dimensional flips, and the theory of elliptic fibrations. The authors - including a;

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Potato Varieties

Originally published in 1926, this book describes the varieties of potato prevalent in the UK in the early twentieth century. Salaman also;

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Rational Points and Arithmetic of Fundamental Groups

Brauer-Manin obstruction is the only one against rational points on curves. This monograph begins by laying the foundations for the space;

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London Mathematical Society Lecture Note Series

homotopy approach to the arithmetic of rational points. Furthermore, the reader will find a collection of research articles on algebraic groups and;

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Complex Tori and Abelian Varieties

without the theory being totally trivial. Standard theorems about abelian varieties are proved, and moduli spaces are discussed. Recent results on;

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De Rham Cohomology of Differential Modules on Algebraic Varieties

...A nice feature of the book [is] that at various points the authors provide examples, or rather co;...

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De Rham Cohomology of Differential Modules on Algebraic Varieties

...A nice feature of the book [is] that at various points the authors provide examples, or rather co;...

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The Brauer-Grothendieck Group

study of rational points on varieties over global fields. The birational invariance of the Brauer group was recently used in a novel way to;

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Cohomology of Drinfeld Modular Varieties, Part 1, Geometry, Counting of Points and Local Harmonic Analysis

Originally published in 1995, Cohomology of Drinfeld Modular Varieties aimed to provide an introduction, in two volumes, both to this;

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