## References for etale cohomology and related topics (Fall 2011)

Other/better references on these topics are welcome.
#### Etale, flat, smooth, unramified morphisms

Chapter 2 of the Neron models book
Chapters 1 through 4 of SGA1
Stacks project chapter on etale morphisms
EGA 4, in all four parts
#### Descent theory

Vistoli's notes on descent theory
Chapter 6 of the Neron models book
Grothendieck's expose on flat descent
Stacks project chapter on descent
#### Sites and topoi

Artin's notes on Grothendieck topologies
SGA 4, tome 1; all available here
Stacks project chapters on hypercoverings, cohomology of sheaves, and cohomology on sites
Brian Conrad's notes on cohomological descent. This theory is a generalisation of Cech theory to allow fairly general morphisms, and was used originally to compute the cohomology of an arbitrary complex variety in terms of smooth projective ones by Deligne
Deligne's notes on cohomological descent, written by Saint-Donat in SGA 4 (tome 2, expose V, bis)
Artin's paper "On joins of hensel rings" is an algebra paper, but it proves (amongst other things) that Cech cohomology computes derived functor cohomology for the etale topology on reasonable schemes (needs ScienceDirect)
Mumford's paper describes what Grothendieck topologies are, and how one can do geometry with them, especially in the context of moduli of curves
Illusie's expository article on topoi
Jacob Lurie's "short" article on higher topoi
#### Constructible sheaves ???

#### Notes, textbooks, and papers on etale cohomology proper

SGA 4.5; available here
SGA 4, tome 2 and 3; all available here
Milne's lecture notes
Milne's textbook
Freitag-Kiehl
"Introduction to etale cohomology" by Tamme
de Jong's lecture notes
Verdier's proof of the duality theorem (in "Proceedings of a conference on Local Fields" at Drierbergen)
Lecture notes from the Woodshole program
Illusie's notes on Gabber's recent finiteness theorems for etale cohomology

Illusie's historical notes on Grothendieck and etale cohomology
#### Weil conjectures

Verdier's proof of the trace formula (in "Proceedings of a conference on Local Fields" at Drierbergen)
Dwork's proof of the rationality of the zeta function (in "Proceedings of a conference on Local Fields" at Drierbergen)
Deligne's Weil 1
Kowalski's notes on Weil 1
Deligne's Weil 2
Katz and Messing's paper deducing purity theorems for crystalline cohomology from Deligne's theorems
Katz's notes on Weil 2 from the Arizona Winter School
Katz's notes on Weil 2 from a 1974 class at Princeton
"Weil conjectures, perverse sheaves and l'adic Fourier transform" by R. Kiehl and R. Wiessauer
Beilinson's lectures at the University of Chicago
Mustaţă book on zeta functions
#### Brauer groups

Grothendieck's exposes 1 and 2
Serre's exposes (especially II and II')
de Jong's notes provide an elegant approach to Brauer groups via the language of twisted sheaves, and also give a new proof of Gabber's result relating the Brauer group to an etale cohomology group
#### Etale fundamental groups

SGA1
Murre's notes (Tata lecture notes)
Grothendieck-Murre book on the tame fundamental group; available through SpringerLink as LNM 208
Lenstra's notes on Galois theory for schemes
#### Etale homotopy theory

Artin-Mazur; available through SpringerLink as LNM 100
Friedlander's book on etale homotopy for simplicial schemes
Artin-Mazur survey article (in "Proceedings of a conference on Local Fields" at Drierbergen)
#### Homological algebra

Gelfand-Manin
Some sections in the Stacks project
Beilinson's lectures at the University of Chicago
Some topological perspectives
#### Some related papers

Serre's paper "Analogues kahleriens de certaines conjectures de Weil." (needs Jstor)
Quillen's paper titled "Some remarks on etale homotopy theory and a conjecture of Adams." in Topology (needs ScienceDirect)
Mazur's notes on relating Tate duality for global fields to the general theory of Verdier duality in the etale topology