Conjectures and results on modular representations of $\mathrm{GL}_n (K)$ for a $p$-adic field $K$
Résumé
Let $p$ be a prime number and $K$ a finite extension of $\mathbb{Q}_p$. We state conjectures on the smooth representations of $\mathrm{GL}_n (K)$ that occur in spaces of mod $p$ automorphic forms (for compact unitary groups). In particular, when $K$ is unramified, we conjecture that they are of finite length and predict their internal structure (extensions, form of subquotients) from the structure of a certain algebraic representation of $\mathrm{GL}_n$. When $n = 2$ and $K$ is unramified, we prove several cases of our conjectures, including new finite length results.
Domaines
Théorie des nombres [math.NT]| Origine | Fichiers produits par l'(les) auteur(s) |
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