Timeline for Lefschetz fixed point formula: an 'easy' proof; cohomology with compact support
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Sep 9, 2012 at 14:16 | comment | added | Mikhail Bondarko | Do you think that the results of Atiyah and Bott can be applied to the Frobenius operator? Which section could help here? | |
| Sep 9, 2012 at 13:18 | answer | added | Steven Landsburg | timeline score: 1 | |
| Sep 9, 2012 at 12:50 | comment | added | Damian Rössler | I mean the paper "A Lefschetz Fixed Point Formula for Elliptic Complexes: II. Applications", Annals of Math. (1968). About the non-proper version: I don't think that there is a version of the LFPF in the non-proper situation. Nevertheless, in that situation, in positive characteristic, there is a conjecture of Deligne saying that if a correspondence is sufficiently twisted by the Frobenius, then there is no "contribution from $\infty$" (ie from the boundary of a compactification). This was proved by Pink and Fujiwara. See Fujiwara "Rigid geometry..." Invent. Math. 127 (1997). | |
| Sep 9, 2012 at 9:41 | comment | added | Mikhail Bondarko | I am sorry; which paper of Atiyah and Bott are you speaking about? I definitely do not want to apply any analytic methods. By non-proper version I mean the version for non-proper (and non-projective) varieties; it involves cohomology with compact support. | |
| Sep 9, 2012 at 9:28 | comment | added | Damian Rössler | What do you mean by the non-proper version ? The LFPF for the Frobenius endomorphism ? As to an 'easy explanation', the paper by Atiyah and Bott on the LFPF outlines an axiomatic approach. | |
| Sep 9, 2012 at 8:53 | history | asked | Mikhail Bondarko | CC BY-SA 3.0 |