Diagrams in the mod p cohomology of Shimura curves. (7th August 2021)
- Record Type:
- Journal Article
- Title:
- Diagrams in the mod p cohomology of Shimura curves. (7th August 2021)
- Main Title:
- Diagrams in the mod p cohomology of Shimura curves
- Authors:
- Dotto, Andrea
Le, Daniel - Abstract:
- Abstract: We prove a local–global compatibility result in the mod $p$ Langlands program for $\mathrm {GL}_2(\mathbf {Q}_{p^f})$ . Namely, given a global residual representation $\bar {r}$ appearing in the mod $p$ cohomology of a Shimura curve that is sufficiently generic at $p$ and satisfies a Taylor–Wiles hypothesis, we prove that the diagram occurring in the corresponding Hecke eigenspace of mod $p$ completed cohomology is determined by the restrictions of $\bar {r}$ to decomposition groups at $p$ . If these restrictions are moreover semisimple, we show that the $(\varphi, \Gamma )$ -modules attached to this diagram by Breuil give, under Fontaine's equivalence, the tensor inductions of the duals of the restrictions of $\bar {r}$ to decomposition groups at $p$ .
- Is Part Of:
- Compositio mathematica. Volume 157:Number 8(2021)
- Journal:
- Compositio mathematica
- Issue:
- Volume 157:Number 8(2021)
- Issue Display:
- Volume 157, Issue 8 (2021)
- Year:
- 2021
- Volume:
- 157
- Issue:
- 8
- Issue Sort Value:
- 2021-0157-0008-0000
- Page Start:
- 1653
- Page End:
- 1723
- Publication Date:
- 2021-08-07
- Subjects:
- Galois representations -- mod p Langlands program
11F80 -- 11S37 -- 22E50
Mathematics -- Periodicals
510 - Journal URLs:
- http://journals.cambridge.org/action/displayJournal?jid=COM ↗
- DOI:
- 10.1112/S0010437X21007375 ↗
- Languages:
- English
- ISSNs:
- 0010-437X
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library DSC - 3366.000000
British Library STI - ELD Digital Store - Ingest File:
- 23513.xml