Report
On locally analytic vectors of the completed cohomology of modular curves
| العنوان: | On locally analytic vectors of the completed cohomology of modular curves |
|---|---|
| المؤلفون: | Pan, Lue |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, Mathematics - Algebraic Geometry, Mathematics - Representation Theory, 11F77 (Primary) 11F22, 11F33, 14G22 (Secondary) |
| الوصف: | We study the locally analytic vectors in the completed cohomology of modular curves and determine the eigenvectors of a rational Borel subalgebra of $\mathfrak{gl}_2(\mathbb{Q}_p)$. As applications, we prove a classicality result for overconvergent eigenforms of weight one and give a new proof of the Fontaine-Mazur conjecture in the irregular case under some mild hypotheses. For an overconvergent eigenform of weight $k$, we show its corresponding Galois representation has Hodge-Tate-Sen weights $0,k-1$ and prove a converse result. Comment: 88 pages; v3: revised version. We incorporate the recent result of Paskunas-Tung (arXiv:2104.08948) |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2008.07099 |
| رقم الانضمام: | edsarx.2008.07099 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |