Timeline for Tannakian criterion for reducedness of Tannakian dual group
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Dec 1 at 1:59 | comment | added | anon | I agree with Angelo: the final statement in the above answer is false. | |
| Apr 20, 2020 at 8:55 | comment | added | Angelo | I don't understand the application of Serre's criterion. For example, $\mu_p$ is not smooth in characteristic $p$, but the category of representations is semisimple. | |
| Mar 31, 2020 at 22:05 | comment | added | Christopher Marlowe | This is quite clever! In the application the group scheme isn't algebraic. The calculation of the Ext's (in finitely generated tensor subcategories) looks difficult. I'm stll hoping for something simpler. | |
| Mar 31, 2020 at 5:21 | comment | added | skd | Fair enough. Edited. | |
| Mar 31, 2020 at 5:21 | history | edited | skd | CC BY-SA 4.0 |
added 459 characters in body
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| Mar 31, 2020 at 4:41 | comment | added | Bugs Bunny | I feel cheated by this answer (despite upvoting it). Suppose one "knows" $Rep(G)$ without knowing $G$. Think of some kind of geometric Satake. Is there a clear pathway for checking smoothness of $G$ in this criterion? | |
| Mar 31, 2020 at 2:48 | comment | added | skd | Yes: the dg-category of representations of G, i.e., QCoh(BG), is the Ind-completion of the dg-category of perfect complexes over BG, which is determined by the category of finite-dimensional representations of G. | |
| Mar 31, 2020 at 2:33 | comment | added | Will Sawin | Is the dg-category of representations determined by the category of finite dimensional algebraic representations? | |
| Mar 31, 2020 at 1:17 | history | answered | skd | CC BY-SA 4.0 |