All Questions
8 questions
4
votes
1
answer
153
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Semistability of the $\ell$-adic representation of variety with semistable reduction
The question is in the title, but here's some quick background.
It's easy to show (assuming smooth-proper base change) that the $\ell$-adic cohomology of a variety over the fraction field of a DVR ...
- 141
1
vote
0
answers
125
views
Is the Frobenius semisimple on the de-Rham cohomology?
Suppose $K$ is a unramified finite extension of $\mathbb Q_p$, and $X$ is a projective smooth curve defined over $K$. By $p$-adic Hodge theory we know $D_{cris}(H_{et}^i(X,\mathbb Q_p))=H_{dR}^i(X)$. ...
- 785
3
votes
0
answers
232
views
$l$-adic Galois representations factor through a common finite quotient
Let $X$ be a smooth projective geometrically connected variety over $\mathbb{Q}$. Assume that for some $m>0$ we have $h^{i, 2m-i}(X)=0$ unless $i=m$.
Does there exist a number field $E$ such that ...
user158636
1
vote
0
answers
272
views
$p$-adic Galois representation and Étale homology
Let $X$ be a smooth proper scheme over some $p$-adic field $K$. The "usual" way to get a Galois representation out of this is to consider the étale cohomology (either $p$ or $\ell$-adic). ...
- 4,418
2
votes
0
answers
232
views
Berthelot’s comparison theorem and functoriality
Let $A$ be a noetherian $p$-adically complete ring with an ideal $I$ equipped with a PD structure and such that $p$ is nilpotent on $A/I$.
Let $S = \text{Spec}(A)$, $S_0 = \text{Spec}(A/I)$, $Y\to S$ ...
- 181
2
votes
0
answers
141
views
Hodge-Tate weights of etale cohomology groups
Given a smooth algebraic variety $X$ over a number field $F$, its $p$-adic cohomology groups $H^i(X \times_F \bar F, \mathbb Q_p)$ carries an action of $\mathrm{Gal}(\bar F/F)$, which gives a ...
- 453
5
votes
0
answers
278
views
Tate's conjecture and symmetry of Hodge-Tate weights
I'm reading Bellaiche's notes on the Block-Kato conjecture (Hawaii summer school). Here is the link http://people.brandeis.edu/~jbellaic/BKHawaii5.pdf
At page 10 he claims that an indirect ...
- 231
5
votes
2
answers
2k
views
Hodge-Tate weights of etale cohomology
Let $K/\mathbb Q_p$ be a local field, $X/K$ a proper scheme with semi-stable reduction.
Question: What is the possible range of Hodge-Tate weights of the etale cohomology $H^i(X_{\overline K}, \...
- 1,503