most recent 30 from http://mathoverflow.net 2013-05-25T09:43:18Z http://mathoverflow.net/feeds/question/16760 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/16760/cohomology-of-sheaves-for-sites-and-galois-cohomology nicojo 2010-03-01T15:18:04Z 2010-03-01T23:50:54Z

<p>Hello,</p> <p>I am looking for a reference (if it exists) that makes the link between cohomology of sheaves for sites and Galois cohomology : </p> <p>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.</p> <p>By the way, what is a reference for cohomology of sites ?</p> <p>Thanks</p>

http://mathoverflow.net/questions/16760/cohomology-of-sheaves-for-sites-and-galois-cohomology/16761#16761 Mariano Suárez-Alvarez 2010-03-01T16:04:05Z 2010-03-01T17:35:00Z

<p>The two references from my comment above, now with links!</p> <ul> <li>Milne, James S. Étale cohomology. Princeton Mathematical Series, 33. Princeton University Press, Princeton, N.J., 1980. xiii+323 pp. <a href="http://www.ams.org/mathscinet-getitem?mr=MR0559531" rel="nofollow">MR0559531</a> You can get another set of notes on étale cohomology from his <a href="http://www.jmilne.org/math/CourseNotes/lec.html" rel="nofollow">web page</a>: «in comparison with my book, the emphasis is on heuristic arguments rather than formal proofs and on varieties rather than schemes».</li> <li>Tamme, Günter. Introduction to étale cohomology. Translated from the German by Manfred Kolster. Universitext. Springer-Verlag, Berlin, 1994. x+186 pp. <a href="http://www.ams.org/mathscinet-getitem?mr=MR1317816" rel="nofollow">MR1317816</a></li> </ul>

http://mathoverflow.net/questions/16760/cohomology-of-sheaves-for-sites-and-galois-cohomology/16766#16766 Frank 2010-03-01T17:17:06Z 2010-03-01T17:17:06Z

<p>I will also add:</p> <p>E. Freitag, R. Kiehl: "Etale cohomology and the Weil conjectures"</p> <p>There are also some notes for a course by de Jong given at Columbia University which can be found here: </p> <p><a href="http://math.columbia.edu/~pugin/Teaching/Etale.html" rel="nofollow">http://math.columbia.edu/~pugin/Teaching/Etale.html</a></p>

http://mathoverflow.net/questions/16760/cohomology-of-sheaves-for-sites-and-galois-cohomology/16807#16807 K.J. Moi 2010-03-01T23:50:54Z 2010-03-01T23:50:54Z

<p>Barry Mazur has also written an article about this: <a href="http://modular.math.washington.edu/edu/2010/582e/refs/mazur-notes_on_etale_cohomology_of_number_fields_original.pdf" rel="nofollow">Notes on étale cohomology of number fields</a>. I hope this helps.</p>