Is there good reference for general theory.of etale cohomology on stacks and more advanced topics? Thanks
$\begingroup$
$\endgroup$
5
-
2$\begingroup$ @ArunDebray Unfortunately, the etale cohomology chapter of the stacks project stacks.math.columbia.edu/tag/03N1 covers only schemes, and the cohomology of stacks chapter stacks.math.columbia.edu/tag/073P covers only sheaves of $\mathcal O_X$-modules. $\endgroup$– Will SawinCommented Apr 28, 2017 at 17:32
-
3$\begingroup$ You can look at "Champs algébriques" by Laumon & Moret-Bailly for a discussion of the lisse-etale site and it's cohomology, and also some papers of Olsson which fixed problems with this. I'll let experts comment further if they want. $\endgroup$– Donu ArapuraCommented Apr 28, 2017 at 19:34
-
1$\begingroup$ that is written in French, may not be convenient. $\endgroup$– Hao YuCommented Apr 28, 2017 at 23:21
-
1$\begingroup$ You can try looking at the series of papers by Laszlo and Olsson. $\endgroup$– nafCommented Apr 29, 2017 at 6:45
-
$\begingroup$ The L-(M-B) book has a serious error, and does not address some of the fundamental theorems of etale cohomology which are proved via Chow's lemma (e.g. proper base change). Look at Olsson's paper "Sheaves on Artin Stacks" https://math.berkeley.edu/~molsson/qcohrevised.pdf for an updated treatment that fixes this error, treats some more recent developments, and moreover is in English. $\endgroup$– dorebellCommented Oct 23, 2017 at 10:48
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
If you have the stomach for technical stuff, I highly recommend the treatment in Gaitsgory-Lurie's article on Tamagawa numbers over function fields:
http://www.math.harvard.edu/~lurie/papers/tamagawa-abridged.pdf
This is section 3.2 and everything is actually done from scratch.
answered Jun 13, 2017 at 3:39