Timeline for Bloch–Beilinson conjecture for varieties over function fields of positive characteristic
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 15 at 18:24 | vote | accept | Bma | ||
| May 15 at 18:24 | |||||
| May 15 at 18:24 | history | bounty ended | Bma | ||
| May 13 at 20:14 | comment | added | Oli Gregory | Yes I think that’s right, Sreekantan’s article only looks at the case $q-2a\geq 1$. This is because the regulator he constructs basically comes from the boundary map in the localisation sequence. I don’t know a reference for a similar style conjecture when $q-2a=0$ I’m afraid. | |
| May 13 at 19:21 | comment | added | Bma | When $X$ is a variety over a number field, the BB conjecture as stated in Bertolini et al, section 2.1 predicts the order of vanishing of $L(H^{2j-1}(\overline{X}, \mathbb{Q}_\ell), s)$ at $s = j$. In Sreekantan's notation, this function is $\Lambda(X, s)$ as defined at the start of section 7, where we take $q = 2j$. Sreekantan's conjectures seem to only predict the order of vanishing at $s = a$ when $q - 2a \ge 1$, whereas Bertolini et al applies to the case $q - 2a = 0$. So they don't seem to directly overlap. | |
| May 13 at 18:17 | comment | added | Bma | Thank you for the suggestion. This is certainly relevant. I will wait a bit to accept to see if there are other answers. However, I must confess that I do not know enough about higher Chow groups to determine if this conjecture implies the one we get if we just rephrase conjecture 2.1.1 in Bertolini, Darmon and Prasanna in terms of varieties over function fields. It seems difficult to check, but do you have any insight into whether this might be true? | |
| May 13 at 15:41 | history | edited | Oli Gregory | CC BY-SA 4.0 |
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| May 13 at 8:06 | history | answered | Oli Gregory | CC BY-SA 4.0 |