Timeline for Action of automorphisms on cohomology with supports
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| May 1, 2015 at 6:12 | comment | added | Piotr Achinger | Another comment: If $f:X\to X$ is an isomorphism, then $H^n_x(X, f^*(-))$ form a universal $\delta$-functor. The system of maps $f^* : H^n_x(X, -)\to H^n_x(X, f^*(-))$ forms a map between two universal $\delta$-functors, so it suffices to check whether $f^*:H^0_x(X, -)\to H^0_x(X, f^*(-))$ is an isomorphism. | |
| May 1, 2015 at 5:18 | history | edited | Amit H | CC BY-SA 3.0 |
added 33 characters in body
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| May 1, 2015 at 5:17 | comment | added | Amit H | You are right. actually in the situation I am looking at M is a sheaf on the category of smooth varieties over k. I have edited the question accordingly. | |
| Apr 30, 2015 at 17:41 | comment | added | Piotr Achinger | (An $f:X\to X$ induces maps $H^n_x(X, M)\to H^n_x(X, f^* M)$ and $H^n(X, f_* M)\to H^n(X, M)$ but there is no canonical way of identifying $f^* M$ and $f_* M$ with $M$...) | |
| Apr 30, 2015 at 17:32 | comment | added | Piotr Achinger | How do automorphisms of $X$ act on $H^n_x(X, M)$? | |
| Apr 30, 2015 at 9:15 | history | asked | Amit H | CC BY-SA 3.0 |