André Weil s mathematical work has deeply influenced the mathematics of the twentieth century. Part of a three-volume set, this work collects his papers in chronological order and includes lengthy commentaries on many of the articles written by Weil himself.

From the reviews:

"All of Weil's works except for books and lecture notes are compiled here, in strict chronological order for easy reference.

But the value goes beyond the convenience of easy reference and accessibility. In the first place, these volumes contain several essays, letters, and addresses which were either published in obscure places () or not published at all.

Even more valuable are the lengthy commentaries on many of the articles, written by Weil himself. These remarks serve as a guide, helping the reader place the papers in their proper context. Moreover, we have the rare opportunity of seeing a great mathematician in his later life reflecting on the development of his ideas and those of his contemporaries at various stages of his career.

The sheer number of mathematical papers of fundamental significance would earn Weil's Collected Papers a place in the library of a mathematician with an interest in number theory, algebraic geometry, representations theory, or related areas. The additional import of the mathematical history and culture in these volumes makes them even more essential." Neal Koblitz in Mathematical Reviews

"André Weil's mathematical work has deeply influenced the mathematics of the twentieth century and the monumental (...) "Collected papers" emphasize this influence." O. Fomenko in Zentralblatt der Mathematik

Autorentext
André Weil was born on May 6, 1906 in Paris. After studying mathematics at the École Normale Supérieure and receiving a doctoral degree from the University of Paris in 1928, he held professorial positions in India, France, the United States and Brazil before being appointed to the Institute for Advanced Study, Princeton in 1958, where he remained until he died on August 6, 1998. André Weil's work laid the foundation for abstract algebraic geometry and the modern theory of abelian varieties. A great deal of his work was directed towards establishing the links between number theory and algebraic geometry and devising modern methods in analytic number theory. Weil was one of the founders, around 1934, of the group that published, under the collective name of N. Bourbaki, the highly influential multi-volume treatise Eléments de mathématique.

Zusammenfassung

From the reviews:

"All of Weil's works except for books and lecture notes are compiled here, in strict chronological order for easy reference.

But the value goes beyond the convenience of easy reference and accessibility. In the first place, these volumes contain several essays, letters, and addresses which were either published in obscure places () or not published at all.

Even more valuable are the lengthy commentaries on many of the articles, written by Weil himself. These remarks serve as a guide, helping the reader place the papers in their proper context. Moreover, we have the rare opportunity of seeing a great mathematician in his later life reflecting on the development of his ideas and those of his contemporaries at various stages of his career.

The sheer number of mathematical papers of fundamental significance would earn Weil's Collected Papers a place in the library of a mathematician with an interest in number theory, algebraic geometry, representations theory, or related areas. The additional import of the mathematical history and culture in these volumes makes them even more essential." Neal Koblitz in Mathematical Reviews

"André Weil's mathematical work has deeply influenced the mathematics of the twentieth century and the monumental (...) "Collected papers" emphasize this influence." O. Fomenko in Zentralblatt der Mathematik

Inhalt
Review of Introduction to the theory of algebraic functions, by C. Che valley.- Sur les théorèmes de de Rham.- Sur les formules explicites de la théorie des nombres premiers.- Jacobi sums as Grössencharaktere.- On picard varieties.- Théorie des points proches sur les variétés différentiables.- Remarques sur un mémoire d'hermite.- Mathematical teaching in Universities.- The mathematics curriculum.- Sur les critères d'équivalence en géométrie algébrique.- Footnote to a recent paper.- Number of points of varieties in finite fields.- On the projective embedding of abelian varieties.- Abstract versus classical algebraic geometry.- Poincaré et l'arithmétique.- On algebraic groups of transformations.- On algebraic groups and homogeneous spaces.- On a certain type of characters of the idèle-class group of an algebraic number-field.- On the theory of complex multiplication.- Science Française?.- The field of definition of a variety.- Zum Beweis des Torellischen Satzes.- Hermann Weyl (18851955).- Réduction des formes quadratiques, d'après Minkowski et Siegel.- Groupes des formes quadratiques indéfinies et des formes bilinéaires alternées.- à l'étude des variétés kählériennes (Préface).- On the moduli of Riemann surfaces.- Final report on contract AF 18(603)-57.- Discontinuous subgroups of classical groups.- Adèles et groupes algébriques.- Y. Taniyama.- De la métaphysique aux mathématiques.- Algebras with involutions and the classical groups.- On discrete subgroups of Lie groups.- Organisation et désorganisation en mathématique.- Sur la théorie des formes quadratiques.- On discrete subgroups of Lie groups (II).- Algebraic Geometry.- Remarks on the cohomology of groups.