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7 votes
1 answer
368 views

How large is Dcris of certain twists of modular forms?

I want to determine $\mathrm D_{\mathrm{cris}}$ of certain twists of the Galois representations attached to modular forms. For one particular twist it is not clear to me how $\mathrm D_{\mathrm{cris}}$...
Michael Fütterer's user avatar
6 votes
2 answers
1k views

Topology on $p$-adic period rings in an article by Fontaine, part II

This is a follow-up to this question. See that question for background and relevant notation. In the answer to that question, it is claimed, if I understand the answer correctly, that a basis of ...
DCM's user avatar
  • 217
4 votes
1 answer
302 views

A definition of a (amalgamated) direct sum

I am wondering about a definition of a direct sum in page $31$ of this paper by R. Liu. I am following the notations in page $31$ of the above paper. Let $V$ be a crystalline irreducible ...
MathStudent's user avatar
3 votes
1 answer
329 views

Calculation of Frobenius on de Rham cohomology of elliptic curves with good reduction

I'm reading "An introduction to the theory of $p$-adic representations" by Laurent Berger. In the page 14 it says: Suppose $F$ is an unramified finite extension of $\mathbb Q_p$ and $E$ is ...
Richard's user avatar
  • 775
2 votes
1 answer
402 views

Irreducibility of Tate module (as a Galois representation) of elliptic curves with good reduction

This question is following the previous question. Definitions: Suppose $F$ is an unramified finite extension of $\mathbb Q_p$ and $E$ is an elliptic curve defined over $F$ with good reduction. Denote ...
Richard's user avatar
  • 775