Timeline for Can local duality for elliptic curves be proven with "big rings"?
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| Oct 11, 2011 at 22:59 | comment | added | Marty | It seems that this provides a very good answer to my question, "...can one exhibit (some of) the duality...", with emphasis on "some of". What I find troublesome is that again, one passes to a linear algebraic gadget -- the Tate module here. In so doing, the duality doesn't capture all of $A(K)$, but only $A(K) \otimes_{Z_p} Q_p$. This effectively kills most of the information about $A(Z / pZ)$, as does any linear algebraic gadget with $Q_p$-vector spaces. So I guess I still fantasize about using $B_{dR}$ in a nonlinear way, like considering $A(B_{dR})$ rather than a Tate module. | |
| Oct 11, 2011 at 22:38 | comment | added | Marty | Since I can't seem to find the Grothendieck Festschrift today, I'm looking through the very nice notes of Joel Bellaiche on the Bloch-Kato conjecture. He treats the Bloch-Kato Selmer group in Section 2, including the theorem you mention. I'll keep on reading now... | |
| Oct 11, 2011 at 14:50 | comment | added | Marty | This looks very promising to me -- I'll check out the Grothendieck Festschrift asap. Thanks! | |
| Oct 11, 2011 at 0:15 | history | answered | Rob Harron | CC BY-SA 3.0 |