Timeline for Tangent Space of Picard Scheme
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 2, 2019 at 17:28 | comment | added | PrimeRibeyeDeal | The first two pages of math.stanford.edu/~conrad/248BPage/handouts/pic.pdf may be helpful. | |
| Jul 1, 2019 at 16:40 | comment | added | Samir Canning | Yes. It may be helpful for you to work out the example of a complex torus/abelian variety | |
| Jul 1, 2019 at 16:00 | comment | added | user267839 | @SamirCanning: yes, you refer to the theory of Lie groups,right? There you can endow the tangent space at neutral element $e$ with Lie algebra structure and the exp-map provides a map from the tangent space at $e$ (= induced Lie algebra) to the group back. On the other hand the exponential sequence induces a map $H^1(X, O_X) \to H^1(O, O_X^*)$ where the right object is the Picard group. So intuitively $H^1(X, O_X)$ "sits" on the place of tangent space. Is this the picture you refer? | |
| Jun 30, 2019 at 6:06 | comment | added | Samir Canning | Think about what the exponential map does in differential geometry and then think about what the exponential map coming from the long exact sequence in cohomology of the exponential sequence does. | |
| Jun 30, 2019 at 3:27 | history | asked | user267839 | CC BY-SA 4.0 |