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| You'll find there the three tapescripts which served as the final stone to obtain some degree. The first one is my master's thesis, written in 2021 under the supervision of Pierre Colmez. It introduces to Fontaine's equivalence for \(p\)-adic representations of \(\mathcal{G}_{\mathbb{Q}_p}\), the associated Herr complex and the construction of Colmez's functor for \(\mathrm{GL}_2(\mathbb{Q}_p)\). Then it explains the analoguous constructions for \(\mathrm{GL}_n(\mathbb{Q}_p)\) by Zábrádi. the second one is my introduction to the research field, written in 2022 to obtain my ENS diploma. It is meant to be bachelor-friendly, starting at Galois theory and \(p\)-adic number and trying to naturally shift to local \(p\)-adic Langlands correspondance. Unfortunately, I only wrote it in French. The last one is my PhD thesis, defended in 2025 under the supervision of Pierre Colmez and Antoine Ducros. Its main contributions are an extensive study of \(\mathcal{S}\)-modules over \(R\), Drinfeld's lemma for diamonds over \(\mathbb{F}_q\) and Fontaine multivariable equivalences in the Lubin-Tate setting, then in the plectic setting. |
- (pdf) Master's thesis under the supervision of Pierre Colmez: Théorie des \((\varphi,\Gamma)\)-modules univariables, représentations de \(\mathrm{GL}_2(\mathbb{Q}_p)\) et généralisation à la théorie des \((\varphi,\Gamma)\)-modules multivariables.
- (pdf) Introduction to the research field: Introduction aux correspondances de Langlands locales \(p\)-adiques.
- (pdf) PhD thesis: Équivalences de Fontaine multivariables pour les corps locaux \(p\)-adiques.
| You'll find there a small pile of notes written when a question (often not that hard) occured to me and either I could not find ealisy a proper reference, or I was willing to write some satisfactory proof. Have a walk around and don't hésitate to send me some remarks. |
- (pdf) Note about Galois descent.
- (pdf) Note for condensed mathematics.
- (pdf) Objects in algebraic structure (and diagram frenzy).
- (pdf) Computations of \((\varphi,\Gamma)\)-modules for some non semisimple representations modulo \(p^2\).
- (pdf) Field isomorphisms of \(p\)-adic fields.
- (pdf) Non isomorphic fields with isomorphic additive and multiplicative groups