Timeline for Hypergeometric sheaves on $\mathbb{A}^{1}_{E}$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 6 at 15:49 | comment | added | Will Sawin | $E$ is of the form $\mathbb F_{q'}$ for some power $q'$ of $q$, and one just has to plug $q'$ instead of $q$ into the prior result. | |
| Oct 6 at 14:50 | comment | added | Takatoshi Kashiwara | @WillSawin Hypergeometric sums are previously defined by nontrivial multiplicative characters of $\mathbb{F}_q$, then we deduce there exists a geometrically irreducible $\ell$-adic middle-extension sheaf on $\mathbb{A}^1_{\mathbb{F}_q}$. Next, we define a hypergeometric sum but over $E$, a finite extension of $\mathbb{F}_{q}$. Whether there will lead to the similar result or not? | |
| Oct 6 at 13:51 | comment | added | Will Sawin | The formula appearing in Fig. 1 you link should be basically the same as the formula in Theorem 8.4.2, with slightly different notation. Can you explain what discrepancy you see between them that needs to be dealt with to deduce the existence of the sheaves associated to the $(a,E)$ sum from the Theorem 8.4.2 sum? | |
| S Oct 6 at 12:01 | review | First questions | |||
| Oct 6 at 12:13 | |||||
| S Oct 6 at 12:01 | history | asked | Takatoshi Kashiwara | CC BY-SA 4.0 |