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Hello,

I am looking for a reference (if it exists) that makes the link between cohomology of sheaves for sites and Galois cohomology :

quickly said, I would like to see Galois cohomology (at least in the commutative case) as the cohomology of a sheaf over the étale site of extensions of k.

By the way, what is a reference for cohomology of sites ?

Thanks

flag	asked Mar 1 2010 at 15:18 nicojo 671●4●14

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Milne's notes on étale cohomology. Tamme's book on étale cohomology. – Mariano Suárez-Alvarez Mar 1 2010 at 15:24

Both of Mariano's references are good. Also, there's plenty of lectures notes and unofficial write-ups of this material all over the web. For example, try googling "mcgill seminar on cohomology" (no quotes). – Cam McLeman Mar 1 2010 at 15:37

Pete L. Clark · Accepted Answer · 2010-03-01 17:35:00Z UTC

The two references from my comment above, now with links!

Milne, James S. Étale cohomology. Princeton Mathematical Series, 33. Princeton University Press, Princeton, N.J., 1980. xiii+323 pp. MR0559531 You can get another set of notes on étale cohomology from his web page: «in comparison with my book, the emphasis is on heuristic arguments rather than formal proofs and on varieties rather than schemes».
Tamme, Günter. Introduction to étale cohomology. Translated from the German by Manfred Kolster. Universitext. Springer-Verlag, Berlin, 1994. x+186 pp. MR1317816

Frank · Answer 2 · 2010-03-01 17:17:06Z UTC

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I will also add:

E. Freitag, R. Kiehl: "Etale cohomology and the Weil conjectures"

There are also some notes for a course by de Jong given at Columbia University which can be found here:

http://math.columbia.edu/~pugin/Teaching/Etale.html

answered Mar 1 2010 at 17:17

Frank
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The notes aren't there, but I love the picture. – Tyler Lawson Mar 1 2010 at 18:10

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The notes are there, actually. – José Figueroa-O'Farrill Mar 1 2010 at 18:48

You are correct. I am getting too old to notice links on a webpage. – Tyler Lawson Mar 1 2010 at 18:55

I didn't add a direct link to the notes so as a) people could see the photo b) I could also add SGA4 1/2 to the references :) – Frank Mar 1 2010 at 21:30

K.J. Moi · Answer 3 · 2010-03-01 23:50:54Z UTC

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Barry Mazur has also written an article about this: Notes on étale cohomology of number fields. I hope this helps.

answered Mar 1 2010 at 23:50

K.J. Moi
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A more permanent copy at numdam: numdam.org/item?id=ASENS_1973_4_6_4_521_0 – Regenbogen Mar 2 2010 at 0:00

Cohomology of sheaves for sites and Galois cohomology

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