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Tagged with p-adic-hodge-theory abelian-varieties
5 questions
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Calculation of de Rham cohomology of abelian varieties/ jacobian varieties
It's known that for a elliptic curve like $E:y^2=x(x-1)(x-t)$ we have a basis $\frac{dx}{y}, \frac{xdx}{y}$ for $H_{dR}^1(E)$. But find such a basis is not an easy thing. I wonder for a general ...
3
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Galois invariant of Tate module
Let $K$ be a finite extension of $\mathbb{Q}_p$. Let $V$ be a de Rham representation of $G_K=\operatorname{Gal}(\overline{K}/K)$. By Corollary 3.8.4 of Bloch and Kato - L-functions and Tamagawa ...
9
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Tamagawa numbers
Let $K$ be a finite extension of $\mathbb{Q}_p$ with absolute Galois group $G_K$. Let $A$ be an abelian variety defined over $K$. The (geometric) Tamagawa number is defined as the order of the ...
9
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Morphisms for good reduction are maps respecting filtration
Please see edits below!
So, let $A,A'/K$ be abelian varieties where $K$ is a $p$-adic local field with residue field $k$. Suppose further that they have good reduction with models $\mathscr{A},\...
7
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showing that abelian varieties are de Rham *without* showing that they are crystalline
If $X$ is a smooth projective variety over a $p$-adic field $K$, then Faltings' Theorem says that the etale cohomology of $X_{\overline{K}}$ is crystalline.
There have been various steps towards this ...