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Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
7
votes
1
answer
862
views
local to global Galois representation
Let $\rho_p : \mbox{Gal}(\overline{\mathbb{Q}}_p / {\mathbb{Q}_p}) \to \mbox{GL}_n(\mathbb{Q}_p)$ be a de Rham $p$-adic representation. Can one find a representation $\rho : \mbox{Gal}(\overline{\math …
16
votes
2
answers
2k
views
Period rings for Galois representations
I have some questions concerning period rings for Galois representations.
First, consider the case of $p$-adic representations of the absolute Galois group $G_K$, where $K$ denote a $p$-adic field. A …