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Research Notes in Mathematics


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Lectures on N_X(p)

Lectures on N_X(p)

1st Edition

Jean-Pierre Serre
November 03, 2011

Lectures on NX(p) deals with the question on how NX(p), the number of solutions of mod p congruences, varies with p when the family (X) of polynomial equations is fixed. While such a general question cannot have a complete answer, it offers a good occasion for reviewing various techniques in l-adic...

Topics in Galois Theory

Topics in Galois Theory

2nd Edition

Jean-Pierre Serre
November 02, 2007

This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensions having a given finite group as Galois group. In the first part of the book, classical methods and...

Semigroups for Delay Equations

Semigroups for Delay Equations

1st Edition

Andras Batkai, Susanna Piazzera
May 09, 2005

In most physical, chemical, biological and economic phenomena it is quite natural to assume that the system not only depends on the present state but also on past occurrences. These circumstances are mathematically described by partial differential equations with delay. This book presents, in a...

Computational Aspects of Polynomial Identities

Computational Aspects of Polynomial Identities

1st Edition

Alexei Kanel-Belov, Louis Halle Rowen
February 22, 2005

A comprehensive study of the main research done in polynomial identities over the last 25 years, including Kemer's solution to the Specht problem in characteristic O and examples in the characteristic p situation. The authors also cover codimension theory, starting with Regev's theorem and...

Regular Sequences and Resultants

Regular Sequences and Resultants

1st Edition

Gunter Scheja, Uwe Storch
May 18, 2001

This carefully prepared manuscript presents elimination theory in weighted projective spaces over arbitrary noetherian commutative base rings. Elimination theory is a classical topic in commutative algebra and algebraic geometry, and it has become of renewed importance recently in the context of...

Abelian l-Adic Representations and Elliptic Curves

Abelian l-Adic Representations and Elliptic Curves

1st Edition

Jean-Pierre Serre
November 15, 1997

This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem. The initial chapters are devoted to...

Polynomial Invariants of Finite Groups

Polynomial Invariants of Finite Groups

1st Edition

Larry Smith
April 15, 1995

Written by an algebraic topologist motivated by his own desire to learn, this well-written book represents the compilation of the most essential and interesting results and methods in the theory of polynomial invariants of finite groups. From the table of contents: - Invariants and Relative...

Operator Algebras, Mathematical Physics, and Low Dimensional Topology

Operator Algebras, Mathematical Physics, and Low Dimensional Topology

1st Edition

Richard Herman, Betül Tanbay
November 15, 1993

This volume records the proceedings of an international conference that explored recent developments and the interaction between mathematical theory and physical phenomena....

The Atiyah-Patodi-Singer Index Theorem

The Atiyah-Patodi-Singer Index Theorem

1st Edition

Richard Melrose
March 31, 1993

Based on the lecture notes of a graduate course given at MIT, this sophisticated treatment leads to a variety of current research topics and will undoubtedly serve as a guide to further studies....

Differential Algebras in Topology

Differential Algebras in Topology

1st Edition

David Anik
February 28, 1993

This research monograph in the field of algebraic topology contains many thought-provoking discussions of open problems and promising research directions....

Free Resolutions in Commutative Algebra and Algebraic Geometry

Free Resolutions in Commutative Algebra and Algebraic Geometry

1st Edition

David Eisenbud, Craig Huneke
November 02, 1992

The selected contributions in this volume originated at the Sundance conference, which was devoted to discussions of current work in the area of free resolutions. The papers include new research, not otherwise published, and expositions that develop current problems likely to influence future...

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