Alibris: Arithmetical algebraic geometry

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1	Heights in Diophantine Geometry more books like this by Enrico Bombieri, Walter Gubler add to wishlist Diophantine geometry has been studied by number theorists for thousands of years, since the time of Pythagoras, and has continued to be a rich area of ideas such as Fermat's Last Theorem, and most recently the ABC conjecture. This monograph is a bridge between the classical theory and modern approach via arithmetic geometry. The authors provide a ... see all copies from $58.30! new only from $67.30!
2	Algebraic Geometry and Arithmetic Curves more books like this by Qing Liu add to wishlist This new-in-paperback edition provides a general introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, ... see all copies from $70.06! new only from $70.06! \| SVS
3	Diophantine Geometry: An Introduction more books like this by Marc Hindry, Joseph H Silverman add to wishlist This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises. see all copies from $21.28! new only from $21.37! \| first editions \| SVS
4	Diophantine Geometry more books like this by Marc Hindry, Joseph H Silverman add to wishlist This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises. see all copies from $33.24! new only from $54.58! \| first editions \| SVS
5	Heights of Polynomials and Entropy in Algebraic Dynamics more books like this by Graham Everest, Thomas Ward add to wishlist The main theme of the book is the theory of heights as they appear in various guises. This includes a large body of results on Mahler's measure of the height of a polynomial of which topic there is no book available. The genesis of the measure in a paper by Lehmer is looked at, which is extremely well-timed due to the revival of interest following ... see all copies from $44.03! new only from $44.95! \| first editions \| SVS
6	Modular Forms and Special Cycles on Shimura Curves more books like this by Stephen S Kudla, Michael Rapoport, Tonghai Yang add to wishlist "Modular Forms and Special Cycles on Shimura Curves" is a thorough study of the generating functions constructed from special cycles, both divisors and zero-cycles, on the arithmetic surface "M" attached to a Shimura curve "M" over the field of rational numbers. These generating functions are shown to be the q-expansions of modular forms and ... see all copies from $42.55! new only from $42.55! \| SVS
7	Fundamentals of Diophantine Geometry more books like this by Serge Lang add to wishlist see all copies from $69.75! new only from $72.28! \| SVS
8	Introduction to Arakelov Theory more books like this by Serge Lang add to wishlist Arakelov introduced a component at infinity in arithmetic considerations, thus giving rise to global theorems similar to those of the theory of surfaces, but in an arithmetic context over the ring of integers of a number field. The book gives an introduction to this theory, including the analogues of the Hodge Index Theorem, the Arakelov ... see all copies from $66.03! new only from $66.03! \| first editions \| SVS
9	The Large Sieve and Its Applications: Arithmetic Geometry, Random Walks and Discrete Groups more books like this by Emmanuel Kowalski add to wishlist Among the modern methods used to study prime numbers, the 'sieve' has been one of the most efficient. Originally conceived by Linnik in 1941, the 'large sieve' has developed extensively since the 1960s, with a recent realisation that the underlying principles were capable of applications going well beyond prime number theory. This book develops a ... see all copies from $76.54! new only from $76.54!
10	Lectures on Arakelov Geometry more books like this by C Soule add to wishlist Arakelov theory is a new geometric approach to diophantine equations. It combines algebraic geometry in the sense of Grothendieck with refined analytic tools such as currents on complex manifolds and the spectrum of Laplace operators. It has been used by Faltings and Vojta in their proofs of outstanding conjectures in diophantine geometry. This ... see all copies from $30.14! new only from $32.40! \| SVS
11 view cover	Cohomology of Arithmetic Groups and Automorphic Forms more books like this by Jean-Pierre Labesse (Editor), Joachim Schwermer (Editor) add to wishlist Cohomology of arithmetic groups serves as a tool in studying possible relations between the theory of automorphic forms and the arithmetic of algebraic varieties resp. the geometry of locally symmetric spaces. These proceedings will serve as a guide to this still rapidly developing area of mathematics. Besides two survey articles, the ... see all copies from $31.97! new only from $31.97! \| SVS
12 view cover	Model Theory and Algebraic Geometry more books like this by Elisabeth Bouscaren (Editor) add to wishlist This introduction to the recent exciting developments in the applications of model theory to algebraic geometry, illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang Conjecture starts from very basic background and works up to the detailed exposition of Hrushovski's proof, explaining the necessary tools and results ... see all copies from $34.99! new only from $34.99! \| SVS
13 view cover	Logarithmic Forms and Diophantine Geometry more books like this by A Baker, G Wustholz add to wishlist There is now much interplay between studies on logarithmic forms and deep aspects of arithmetic algebraic geometry. New light has been shed, for instance, on the famous conjectures of Tate and Shafarevich relating to abelian varieties and the associated celebrated discoveries of Faltings establishing the Mordell conjecture. This book gives an ... see all copies from $59.33! new only from $61.42! \| SVS
14 view cover	Galois Representations in Arithmetic Algebraic Geometry more books like this by A J Scholl (Editor), Richard Lawrence Taylor (Editor), N J Hitchin (Editor) add to wishlist This book contains conference proceedings from the 1996 Durham Symposium on 'Galois representations in arithmetic algebraic geometry'. The title was interpreted loosely and the symposium covered recent developments on the interface between algebraic number theory and arithmetic algebraic geometry. The book reflects this and contains a mixture of ... see all copies from $79.91! new only from $79.91! \| SVS
15 view cover	Kolyvagin Systems more books like this by Barry Mazur add to wishlist Since their introduction by Kolyvagin, Euler systems have been used in several important applications in arithmetic algebraic geometry. For a $p$-adic Galois module $T$, Kolyvagin's machinery is designed to provide an upper bound for the size of the Selmer group associated to the Cartier dual $T^$. Given an Euler system, Kolyvagin produces a ... see all copies* from $55.20! new only from $61.34!
16 view cover	Arithmetic Algebraic Geometry more books like this by Brian David Conrad add to wishlist The articles in this volume are expanded versions of lectures delivered at the Graduate Summer School and at the Mentoring Program for Women in Mathematics held at the Institute for Advanced Study/Park City Mathematics Institute. The theme of the program was arithmetic algebraic geometry. The choice of lecture topics was heavily influenced by the ... see all copies from $84.48! new only from $84.48!
17 view cover	Arithmetic Algebraic Geometry: Lectures Given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) Held in Trento, Italy, June 24-July 2, 1991 more books like this by J -L Colliot-Thelene add to wishlist The papers contained in this volume survey the connection between algebraic K-theory and the torsion algebraic cycles on an algebraic variety, introduce an approach to Iwasawa theory for Hasse-Weil L-function, and demonstrate applications of arithmetic geometry to Diophantine approximation. see all copies from $31.97! new only from $31.97! \| SVS
18	An invitation to arithmetic geometry more books like this by Dino Lorenzini add to wishlist In this volume the author gives a unified presentation of some of the basic tools and concepts in number theory, commutative algebra, and algebraic geometry, and for the first time in a book at this level, brings out the deep analogies between them. The geometric viewpoint is stressed throughout the book. Extensive examples are given to illustrate ... see all copies from $62.54! new only from $70.37!
19 view cover	Computational Arithmetic Geometry: Ams Special Session on Computational Arithmetic Geometry, April 29-30, 2006, San Francisco State University, San Francisco, CA more books like this by Kristin E Lauter add to wishlist With the recent increase in available computing power, new computations are possible in many areas of arithmetic geometry. To name just a few examples, Cremona's tables of elliptic curves now go up to conductor 120,000 instead of just conductor 1,000, tables of Hilbert class fields are known for discriminant up to at least 5,000, and special ... see all copies from $32.83! new only from $32.83!
20 view cover	P-Adic Geometry: Lectures from the 2007 Arizona Winter School more books like this by Matthew Baker add to wishlist In recent decades, $p$-adic geometry and $p$-adic cohomology theories have become indispensable tools in number theory, algebraic geometry, and the theory of automorphic representations. The Arizona Winter School 2007, on which the current book is based, was a unique opportunity to introduce graduate students to this subject. Following invaluable ... see all copies from $57.69! new only from $57.69!
21 view cover	Hilbert Modular Forms: Mod P and P-Adic Aspects more books like this by F Andreatta add to wishlist We study Hilbert modular forms in characteristic $p$ and over $p$-adic rings. In the characteristic $p$ theory we describe the kernel and image of the $q$-expansion map and prove the existence of filtration for Hilbert modular forms; we define operators $U$, $V$ and $\Theta_\chi$ and study the variation of the filtration under these operators. Our ... see all copies from $22.50! new only from $62.98! \| first editions
22 view cover	Arithmetic Geometry more books like this by F Catanese (Editor) add to wishlist Brought together in this book are papers from a conference on arithmetic geometry held in Cortona. The contributions are from many of the leading authorities in this field and together they cover a wide spectrum of topics that give an unsurpassed overview of research into number theory, geometry and their interactions. All whose research interests ... see all copies from $15.00! new only from $27.00! \| first editions
23	An Arithmetic Riemann-Roch Theorem for Singular Arithmetic Surfaces more books like this by Wayne Aitken add to wishlist see all copies from $61.00! new only from $61.00!
24 view cover	Arithmetic Differential Equations more books like this by Alexandru Buium add to wishlist This monograph contains exciting original mathematics that will inspire new directions of research in algebraic geometry. Developed here is an arithmetic analog of the theory of ordinary differential equations, where functions are replaced by integer numbers, the derivative operator is replaced by a 'Fermat quotient operator', and differential ... see all copies from $109.74! new only from $109.74!
25 view cover	Hilbert's Tenth Problem: Relations with Arithmetic and Algebraic Geometry more books like this by Jan Denef (Editor), Leonard Lipshitz (Editor) add to wishlist This book is the result of a meeting that took place at the University of Ghent (Belgium) on the relations between Hilbert's tenth problem, arithmetic, and algebraic geometry. Included are written articles detailing the lectures that were given as well as contributed papers on current topics of interest. The following areas are addressed: an ... see all copies from $75.00! new only from $75.00!

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