Abstract
Abstract
We prove some qualitative results about the p-adic Jacquet–Langlands correspondence defined by Scholze, in the
$\operatorname {\mathrm {GL}}_2(\mathbb{Q}_p )$
residually reducible case, using a vanishing theorem proved by Judith Ludwig. In particular, we show that in the cases under consideration, the global p-adic Jacquet–Langlands correspondence can also deal with automorphic forms with principal series representations at p in a nontrivial way, unlike its classical counterpart.
Publisher
Cambridge University Press (CUP)
Reference50 articles.
1. [2] Ardakov, K. and Brown, K. A. , Ring-theoretic properties of Iwasawa algebras: A survey, Doc. Math. extra vol. (2006), 7–33.
2. Représentations de $\mathrm{GL}_2\left(\mathbb{Q}{p}\right)$et $\left(\varphi, \varGamma \right)$-modules;Colmez;Astérisque,2010
3. The $p$-adic local Langlands correspondence for ${\rm GL}_2(\mathbb{Q}_p)$
4. Completed cohomology of Shimura curves and a p-adic Jacquet–Langlands correspondence
5. SUR QUELQUES REPRÉSENTATIONS MODULAIRES ET $p$-ADIQUES DE $\mathrm{GL}_2(\bm{Q}_{p})$. II
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献