Algebraic geometry

This book introduces the theory of complex surfaces through a comprehensive look at finite covers of the projective plane branched along line arrangements.

Over the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights.

In the earlier monograph Pseudo-reductive Groups, Brian Conrad, Ofer Gabber, and Gopal Prasad explored the general structure of pseudo-reductive groups.

Descent in Buildings begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings.

A look at one of the most exciting unsolved problems in mathematics todayElliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics-the Birch and Swinnerton-Dyer Conjecture.

Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view.

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance.

Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices.

Explores connections between infinitary model theory and other branches of mathematical logic, with algebraic applications.

Explores connections between infinitary model theory and other branches of mathematical logic, with algebraic applications.

Formal development of the mathematical theory of quantum information with clear proofs and exercises.

An up-to-date, panoramic account of the theory of random walks on groups and graphs, outlining connections with various mathematical fields.

An up-to-date, panoramic account of the theory of random walks on groups and graphs, outlining connections with various mathematical fields.

An up to date study of recent progress in vector bundle methods in the representation theory of elementary abelian groups.

An up to date study of recent progress in vector bundle methods in the representation theory of elementary abelian groups.

Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.

Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.

This study of graded rings includes the first systematic account of graded Grothendieck groups.

The first comprehensive and up-to-date account of discriminant equations and their applications.

This study of graded rings includes the first systematic account of graded Grothendieck groups.

The first comprehensive and up-to-date account of discriminant equations and their applications.

Forming the basis of a second course in algebraic geometry, this book explains key ideas, each illustrated with abundant examples.

Forming the basis of a second course in algebraic geometry, this book explains key ideas, each illustrated with abundant examples.

A unified account of a powerful classical method, illustrated by applications in number theory.

A unified account of a powerful classical method, illustrated by applications in number theory.

Describes how to use coherent sheaves and cohomology to prove combinatorial and number theoretical identities over finite fields.

Describes how to use coherent sheaves and cohomology to prove combinatorial and number theoretical identities over finite fields.

Combines cutting-edge research and expository articles in Hodge theory.

Combines cutting-edge research and expository articles in Hodge theory.

This third volume of four describes all the most important techniques, mainly based on Gröbner bases.

This third volume of four describes all the most important techniques, mainly based on Gröbner bases.

A comprehensive collection of expository articles on cutting-edge topics at the forefront of research in algebraic geometry.

A comprehensive collection of expository articles on cutting-edge topics at the forefront of research in algebraic geometry.

A comprehensive introductory monograph on the theory of aperiodic order, with numerous illustrations and examples.

A comprehensive introductory monograph on the theory of aperiodic order, with numerous illustrations and examples.

This book provides a largely self-contained introduction to Cox rings and their applications in algebraic and arithmetic geometry.

This book provides a largely self-contained introduction to Cox rings and their applications in algebraic and arithmetic geometry.

This book presents a coherent suite of computational tools for the study of group cohomology algebraic cycles.

This book presents a coherent suite of computational tools for the study of group cohomology algebraic cycles.

The thoroughly revised and updated second edition of this acclaimed text has several new and expanded sections and more than 1,100 exercises.

This popular graduate text has been thoroughly revised and updated to incorporate recent developments in the field.

The thoroughly revised and updated second edition of this acclaimed text has several new and expanded sections and more than 1,100 exercises.

This popular graduate text has been thoroughly revised and updated to incorporate recent developments in the field.

The second of two volumes offering a modern account of Kaehlerian geometry and Hodge theory for researchers in algebraic and differential geometry.

The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure written for students.

Explains both the how and the why of linear algebra to get students thinking like mathematicians.

Explains both the how and the why of linear algebra to get students thinking like mathematicians.

This detailed exposition makes classical algebraic geometry accessible to the modern mathematician.

This friendly introduction helps undergraduate students understand and appreciate matroid theory and its connections to geometry.

A complete and accessible introduction to the study of arithmetic differential operators over the p-adic integers.