Timeline for Why does the naive definition of compactly supported étale cohomology give the wrong answer?
Current License: CC BY-SA 2.5
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| Apr 12, 2010 at 3:09 | comment | added | BCnrd | Here's an amusing point about Verdier-Poincare duality. In Verdier's article in the Dreibergen book, he gives a beautiful reduction to the special case of degree-1 cohomology for constant coefficients for a smooth proper curve over an algebraically closed field. That case he passes over in silence, yet it does require some actual work (e.g., it is not by definition that it meshes well with Weil pairing on principally polarized Jacobian when char. > 0). | |
| Apr 12, 2010 at 1:49 | vote | accept | Sam Derbyshire | ||
| Apr 12, 2010 at 1:49 | comment | added | Sam Derbyshire | Thanks for the answer! I had actually read the corresponding section in your book "Etale cohomology", where it was only remarked that the usual definition is "uninteresting"; the details here are much more enlightening. I'm still curious as to why this happens - it seems like these must be (honest) derived functors somehow, even though there seems no way to define them independent of a compactification - but it does give some reason for the difficulty of proving Verdier duality in the étale setting. | |
| Apr 12, 2010 at 1:28 | history | edited | JS Milne | CC BY-SA 2.5 |
edited body; added 251 characters in body
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| Apr 12, 2010 at 1:21 | history | answered | JS Milne | CC BY-SA 2.5 |