All Questions
8 questions
2
votes
0
answers
110
views
Galois action on the cohomology of a curve over a local field with bad reduction
Let $C/\mathbb Q_p$ (or a p-adic local field more generally) be a smooth projective curve with split semistable reduction over $\mathbb Z_p$. What can we say about the action of the Galois group $\...
- 7,746
4
votes
1
answer
184
views
Meaning of dagger cohomology $H^{1 \dagger}(G^\dagger)$ in "Frobenius and Monodromy Operators" by Coleman and Iovita
Let $G$ be an abelian variety with good reduction over a finite extension $K$ of $\mathbb{Q}_p$. In equation (2.4) on page 179 of my edition of "The Frobenius and monodromy operators for curves ...
- 658
3
votes
1
answer
385
views
Overconvergent modular forms and the level at $p$
I am a little bit confused about the basic theory of overconvergent modular forms, so here is a question that I think will be straightforward for those who know the theory but would help me a lot.
The ...
- 241
32
votes
1
answer
8k
views
$p$-adic Hodge Theory for rigid spaces, after P. Scholze
I was going over P. Scholze's paper on $p$-adic Hodge Theory for rigid analytic varieties.
This question is around the "Poincaré Lemma" in the paper.
Throughout, let $X$ be a proper smooth rigid ...
user113453
41
votes
2
answers
3k
views
Perfectoid universal covers
It is often said, with varying degrees of rigor or enthusiasm, that every rigid space (say over $\mathbb{C}_p$) has a pro-etale cover which is 'topologically trivial' in some sense. For example, this ...
- 843
3
votes
1
answer
312
views
Geometric line bundles on the Tate curve
Let $E_q$ be the rigid analytic Tate elliptic curve over a complete algebraically closed non-archimedean field $K$ of mixed characteristic $(0,p)$, with parameter $q\in K^{\times}$ with $|q|<1$.
...
user178246
7
votes
1
answer
480
views
Rigid versus log-rigid cohomology for semistable varieties
If $K$ is a p-adic field, with maximal unramified subfield $K_0$, and $X$ is a proper semi-stable $O_K$-scheme, then there's a canonical way to make the special fibre $X_k$ into a log-scheme; and ...
- 37k
23
votes
1
answer
1k
views
function field analogy and global/absolute geometry
The "function field analogy" seems to be a topic that is considerably bigger than any one existing writeup conveys. There are several old question on MO and and MathSE that ask for details. One of the ...
- 19.9k