## $p$-adic local Langlands for $\mathrm{GL}_2(\mathbb{Q}_p)$ study group

In Summer 2020 Andrew Graham and I ran a study group on Paškūnas's paper [Paš2] and related topics. Notes, slides, and videos are included below.

Speaker | Date | Topic | Notes | References |
---|---|---|---|---|

Study group plan | See PDF | |||

Abi | May 1, 2020 | Mod $p$ and integral $p$-adic representations of $\mathrm{GL}_n(\mathbb{Q}_p)$ | Notes | [Eme1], [Her1], [New] |

Ashwin | May 8, 2020 | Irreducible smooth admissible mod $p$ representations of $\mathrm{GL}_n(F)$ | Notes | [AHHV], [Bre], [GK], [Her2], [Her3] |

Andy | May 15, 2020 | Ext groups between irreducible representations | Typed notes and written notes | [Eme2], [Oll], [Paš1], [Vig] |

Ashvni | May 22, 2020 | Banach $L$-representations | Slides and handwritten proofs | [Paš2] |

Pol | May 28, 2020 | Locally finite abelian categories | Video (caution, big file) | [Gab] |

Ashwin | June 5, 2020 | Paškūnas's deformation theory | Notes | [Paš2] |

Sam | June 19, 2020 | Galois representations and phi-gamma modules | Notes and Video (pw: 2g@0M%8#) | [Ber] |

Waqar | June 26, 2020 | Colmez's Montréal Functor | [Col] | |

Ashwin | July 31, 2020 | Deformation Theory for Supersingular Representations | Notes and video | [Kis], [Paš1], [Paš2] |

## References

- [AHHV] Abe, Henniart, Herzig, Vignéras, A classification of irreducible admissible mod $p$ representations of $p$-adic reductive groups
- [Ber] Berger, Galois Representations and $(\varphi, \Gamma)$-modules (L14-L18)
- [Bre] Breuil, Sur quelques représentations modulaires et $p$-adiques de $\mathrm{GL}_2(\mathbb{Q}_p)$: I
- [Col] Colmez, Représentations de $\mathrm{GL}_2(\mathbb{Q}_p$ et $(\varphi, \Gamma)$-modules
- [Eme1] Emerton, Ordinary Parts of Admissible Representations of $p$-adic Reductive Groups I: Definition and First Properties
- [Eme2] Emerton, Ordinary Parts of Admissible Representations of $p$-adic Reductive Groups II: Derived functors
- [Gab] Gabriel, Des catégories abéliennes
- [GK] Grosse-Klönne, On special representations of $p$-adic reductive groups
- [Her1] Herzig, $p$-modular and locally analytic representation theory of $p$-adic groups
- [Her2] Herzig, The classification of irreducible admissible mod $p$ representations of a $p$-adic $\mathrm{GL}_n$
- [Her3] Herzig, A Satake isomorphism in characteristic $p$
- [Kis] Kisin, Deformations of $G_{\mathbb{Q}_p}$ and $\mathrm{GL}_2(\mathbb{Q}_p)$ representations
- [New] Newton, LTCC Course: Representations of $p$-adic groups
- [Oll] Ollivier, Le foncteur des invariants sous l’action du pro-$p$-Iwahori de $\mathrm{GL}_2(F)$
- [Paš1] Paškūnas, Extensions for supersingular representations of $\mathrm{GL}_2(\mathbb{Q}_p)$
- [Paš2] Paškūnas, The image of Colmez's Montréal functor
- [Vig] Vignéras, Representations modulo $p$ of the p-adic group $\mathrm{GL}(2, F)$