${\mathcal{L}}$ -INVARIANTS AND LOCAL–GLOBAL COMPATIBILITY FOR THE GROUP $\text{GL}_{2}/F$
Let $F$ be a totally real number field, ${\wp}$ a place of...
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2016-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509416000098/type/journal_article |
| Summary: | Let
$F$
be a totally real number field,
${\wp}$
a place of
$F$
above
$p$
. Let
${\it\rho}$
be a
$2$
-dimensional
$p$
-adic representation of
$\text{Gal}(\overline{F}/F)$
which appears in the étale cohomology of quaternion Shimura curves (thus
${\it\rho}$
is associated to Hilbert eigenforms). When the restriction
${\it\rho}_{{\wp}}:={\it\rho}|_{D_{{\wp}}}$
at the decomposition group of
${\wp}$
is semistable noncrystalline, one can associate to
${\it\rho}_{{\wp}}$
the so-called Fontaine–Mazur
${\mathcal{L}}$
-invariants, which are however invisible in the classical local Langlands correspondence. In this paper, we prove one can find these
${\mathcal{L}}$
-invariants in the completed cohomology group of quaternion Shimura curves, which generalizes some of Breuil’s results [Breuil, Astérisque, 331 (2010), 65–115] in the
$\text{GL}_{2}/\mathbb{Q}$
-case. |
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| ISSN: | 2050-5094 |