Explicit reduction modulo \(p\) of certain 2-dimensional crystalline representations. II. (English) Zbl 1305.11046
Summary: We complete the calculations begun by the authors in [Int. Math. Res. Not. 2009, No. 12, 2303-2317 (2009; Zbl 1189.11054)], using the \(p\)-adic local Langlands correspondence for \(\mathrm{GL}_2(\mathbb Q_{p})\) to give a complete description of the reduction modulo \(p\) of the 2-dimensional crystalline representations of \(G_{\mathbb Q_p}\) of slope less than 1, when \(p > 2\).
MSC:
| 11F80 | Galois representations |
| 11F33 | Congruences for modular and \(p\)-adic modular forms |
| 11S37 | Langlands-Weil conjectures, nonabelian class field theory |
