Timeline for Modern integral $p$-adic Hodge theory and modularity lifting and Fontaine-Mazur
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 27 at 6:11 | comment | added | David Loeffler | (typo in first comment: "did not stand still" should be "stood still".) | |
| Jun 27 at 6:10 | comment | added | David Loeffler | Your two example citations are (a) a set of introductory lecture notes which deliberately uses non-cutting-edge methods for simplicity, and (b) a paper somewhat outside the mainstream of research in this area. For instance, Kisin's work on potentially semistable deformation rings – which relies on Breuil-Kisin modules to go well beyond the Fontaine--Laffaille range – has been fundamental to virtually every major advance in modularity lifting since it was written (in 2007). | |
| Jun 27 at 6:03 | comment | added | David Loeffler | I disagree with the premise of this question. You seem to suggest that integral p-adic HT did not stand still in the multiple decades between Fontaine--Laffaille and Bhatt--Scholze, and many of those advances (e.g. Breuil-Kisin modules) were motivated by & immediately applied to modularity-lifting problems. | |
| Jun 25 at 21:50 | comment | added | coLaideronnette | On the other hand, the modern results on automorphy lifting theorems are heavily dependent on the study of the geometry of Shimura varieties, where the $p$-adic geometry plays an essential role. | |
| Jun 25 at 21:36 | comment | added | coLaideronnette | From the arithmetic perspective, (integral) $p$-adic Hodge theory is the study of $p$-adic Galois representations. That’s why it plays a role in the proof of automorphy lifting theorems. However, Bhatt-Morrow-Scholze‘s work is geometric i.e. to study the geometry of (proper smooth) schemes over a $p$-adic field. So they are not directly related but we can construct some functors to link them and study $p$-adic Hodge theory via the interplay between the arithmetic and geometric perspectives. | |
| Jun 25 at 11:11 | history | asked | David Corwin | CC BY-SA 4.0 |