Timeline for Weil pairing as an algebraic cycle?
Current License: CC BY-SA 3.0
3 events
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| Apr 18, 2012 at 10:36 | comment | added | Jason Starr | OP: Can you say more precisely what you are looking for? The Weil pairing is usually thought of as a pairing only on $n$-torsion points taking values in the group of $n^\text{th}$ roots of unity. In what sense would you like to see this as an algebraic cycle? Are you asking how to interpret this as a pairing of the corresponding torsion invertible sheaves (on the respective dual Abelian varieties)? For that, see Deligne's expose in SGA 4. | |
| Apr 17, 2012 at 21:17 | comment | added | Keerthi Madapusi | Do you mean the Poincare pairing between the cohomology of an abelian variety and its dual, or the pairing on the cohomology of an abelian variety induced by the choice of a polarization? I would think the latter is just the polarization pairing attached to the ample line bundle that's giving you the polarization (at least up to sign). | |
| Apr 17, 2012 at 20:26 | history | asked | Adam Harris | CC BY-SA 3.0 |