Timeline for Why is the Tate local duality pairing compatible with the Cartier duality pairing?
Current License: CC BY-SA 3.0
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jul 30, 2014 at 1:25 | vote | accept | Question Mark | ||
| Jul 29, 2014 at 23:58 | comment | added | user27920 | The discussion of Tate's theorem as Theorem 4.1 of Chapter X of Lang's book "Topics in cohomology of groups" (notes that Lang took based on weekly letters he got from Tate in the late 1950's) treats the case of $p$-adic fields (i.e., char. 0). Right at the start occurs the commutative diagram being asked about in this question (with $S = {\rm{Spec}}(K)$ for a $p$-adic field $K$), where it is claimed to hold "by the general theory of the augmented cup product" (no reference provided). So over fields of characteristic 0 there should be a more down-to-earth proof using cocycle calculations. | |
| Jul 29, 2014 at 19:20 | answer | added | user27920 | timeline score: 6 | |
| Jul 29, 2014 at 14:15 | history | edited | Question Mark | CC BY-SA 3.0 |
edited title
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| Jul 29, 2014 at 13:54 | history | asked | Question Mark | CC BY-SA 3.0 |