The many diverse articles presented in these three volumes, collected on the occasion of Alexander Grothendieck's sixtieth birthday and originally published in 1990, were offered as a tribute to one of the world's greatest living mathematicians. Grothendieck changed the very way we think about many branches of mathematics. Many of his ideas, revolutionary when introduced, now seem so natural as to have been inevitable. Indeed, it is difficult to fully grasp the influence his vast contributions to modern mathematics have subsequently had on new generations of mathematicians.

Many of the groundbreaking contributions in these volumes contain material that is now considered foundational to the subject. Topics addressed by these top-notch contributors match the breadth of Grothendieck's own interests, including: functional analysis, algebraic geometry, algebraic topology, number theory, representation theory, K-theory, category theory, and homological algebra.

CONTRIBUTORS to Volume I: A. Altman; M. Artin; V. Balaji; A. Beauville; A.A. Beilinson; P. Berthelot; J.-M. Bismut; S. Bloch; L. Breen; J.-L. Brylinski; J. Dieudonné; H. Gillet; A.B. Goncharov; K. Kato; S. Kleiman; W. Messing; V.V. Schechtman; C.S. Seshadri; C. Soulé; J. Tate; M. van den Bergh; and A.N. Varchenko.

Zusammenfassung

Alexander Grothendieck's sixtieth birthday and originally published in 1990. The articles were offered as a tribute to one of the world's greatest living mathematicians. Many of the groundbreaking contributions in these volumes contain material that is now considered foundational to the subject. Topics addressed by these top-notch contributors match the breadth of Grothendieck's own interests, including: functional analysis, algebraic geometry, algebraic topology, number theory, representation theory, K-theory, category theory, and homological algebra.

CONTRIBUTORS to Volume I: A. Altman; M. Artin; V. Balaji; A. Beauville; A.A. Beilinson; P. Berthelot; J.-M. Bismut; S. Bloch; L. Breen; J.-L. Brylinski; J. Dieudonné; H. Gillet; A.B. Goncharov; K. Kato; S. Kleiman; W. Messing; V.V. Schechtman; C.S. Seshadri; C. Soulé; J. Tate; M. van den Bergh; and A.N. Varchenko.

Inhalt
De L'Analyse Fonctionnelle aux Fondements de la Géométrie Algébrique.- The presentation functor and the compactifled Jacobian.- Some Algebras Associated to Automorphisms of Elliptic Curves.- Cohomology of a Moduli Space of Vector Bundles.- Sur les hypersurfaces dont les sections hyperplanes sont à module constant.- Aomoto Dilogarithms, Mixed Hodge Structures and Motivic Cohomology of Pairs of Triangles on the Plane.- Théorie de Dieudonné cristalline III: théorèmes d'équivalence et de pleine fidélité.- Complex Immersions and Arakelov Geometry.- L-Functions and Tamagawa Numbers of Motives.- Bitorseurs et Cohomologie Non Abélienne.- Non-commutative Ruelle-Sullivan type currents.