Luc Illusie

Fundamental algebraic geometry : Grothendieck's FGA explained

Grothendieck topologies, fibered categories and descent theory: Introduction Preliminary notions Contravariant functors Fibered categories Stacks Construction of Hilbert and Quot schemes: Construction of Hilbert and Quot schemes Local properties and Hilbert schemes of points: Introduction Elementary deformation theory Hilbert schemes of points Grothendiecks existence theorem in formal geometry with a letter of Jean-Pierre Serre: Grothendiecks existence theorem in formal geometry The Picard scheme: The Picard scheme Bibliography Index.

Les suites spectrales associées au complexe de de Rham-Witt

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Odds and Ends on Finite Group Actions and Traces

In this article, we study several problems related to virtual traces for finite group actions on schemes of finite type over an algebraically closed field. We also discuss applications to fixed point sets. Our results generalize previous results obtained by Deligne, Laumon, Serre and others.

Ordinarité des intersections complètes générates

Soient k un corps de caracteristique p > 0, r un entier ≥ 0, et a = (a1,...,am) une suite d’entiers ≥ 1. Notons 5 le k-schema parametrant les intersections completes lisses de dimension r et multidegre a dans ℙkr+m et X → S la famille universelle. Nous prouvons le resultat suivant: Theoreme 0.1. Il existe un ouvert non vide U de S tel que, pour tout s dans U, Xssoit ordinaire.

Grothendieck at Pisa: crystals and Barsotti-Tate groups

Grothendieck visited Pisa twice, in 1966, and in 1969. It is on these occasions that he conceived his theory of crystalline cohomology and wrote foundations for the theory of deformations of p-divisible groups, which he called Barsotti-Tate groups. He did this in two letters, one to Tate, dated May 1966, and one to me, dated Dec. 2–4, 1969. Moreover, discussions with Barsotti that he had during his first visit led him to results and conjectures on specialization of Newton polygons, which he wrote in a letter to Barsotti, dated May 11, 1970.