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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 …
A M's user avatar
  • 657
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 …
A M's user avatar
  • 657