Let F be a totally real field, v an unramified place of F dividing p and (rho) over bar : Gal((Q) over bar /F) -> GL(2) ((F-p) over bar) a continuous irreducible representation such that (rho) over bar vertical bar(Gal((F) over barv/Fv)) is reducible and sufficiently generic. If (rho) over bar is modular (and satisfies some weak technical assumptions), we show how to recover the corresponding extension between the two characters of Gal((F-v) over bar /F-v) in terms of the action of GL(2)(F-v) on the cohomology mod p.
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机译：令F为完全实数场，v的F的无分支位置将p和（rho）除以bar：Gal（（Q）over bar / F）-> GL（2）（（Fp over over bar）连续不可约表示从而使得竖线上的（rho）垂直条（bar（Fv上的Gal（（F）））是可简化的并且足够通用。如果（rho）over bar是模块化的（并且满足一些较弱的技术假设），我们将展示如何根据GL（2）的作用恢复Gal（（Fv）over bar / Fv）两个字符之间的对应扩展。 （Fv）关于同调mod p。
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