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The term Galois representation is frequently used when the G-module is a vector space over a field or a free module over a ring, but can also be used as a synonym for G-module. The study of Galois modules for extensions of local or global fields is an important tool in number theory.

8 votes
1 answer
992 views

Is the Galois x Hecke action on cohomology of Shimura varieties semi-simple?

Given a reductive group $G/\mathbf Q$ (+ additional data), and a compact open subgroup $K\subset G(\mathbf A^\infty)$, there is a standard construction that produces a Shimura variety $S$ and if we ch …
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2 votes
1 answer
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Rapoport-Zink proof of purity of monodromy

Hi, Does anyone know if the article "Über die lokale Zetafunktion von Shimuravarietäten. Monodromiefiltration und verschwindene Zyklen in ungleicher Charakteristik", INvent. Math, 68 (1980) by Rapo …
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