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Results tagged with nt.number-theory
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user 76409
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
7
votes
Applications of $p$-adic Hodge theory
For an example of an application of $p$-adic Hodge theory in a geometric setting, I thoroughly recommend reading the beautiful paper
P. Berthelot, H. Esnault, K. Rulling, Rational points over finite …
6
votes
0
answers
304
views
Geometry of syntomic cohomology
Deligne cohomology has a geometric interpretation. For example, $H^{2}_{\mathcal{D}}(X,\mathbb{Z}(1))$ is identified with the group $H^{1}(X,\mathcal{O}_{X}^{\ast})$ of isomorphism classes of line bun …
- 1,404
5
votes
Accepted
Integral refinements of rigid cohomology
There has been some progress on this question since the question was asked. Apparently it was "known to the experts" that there cannot be an integral $p$-adic cohomology theory which is finitely gener …
- 1,404
6
votes
Accepted
Rigid versus log-rigid cohomology for semistable varieties
$\require{AMScd}$I'll expand a little on my comment to give an answer to David's follow up question:
Firstly, the general relationship is described in Chiarellotto's Duke 1999 paper "Rigid cohomology …
- 1,404
1
vote
Meaning of dagger cohomology $H^{1 \dagger}(G^\dagger)$ in "Frobenius and Monodromy Operator...
I think $X^{\dagger}$ must mean the dagger space associated to the weak formal scheme you get by taking the weak completion of the model $\mathcal{X}$ along the special fibre $\mathcal{X}_{k}$. Then $ …
- 1,404
2
votes
Bloch–Beilinson conjecture for varieties over function fields of positive characteristic
This may not be precisely what you want, but a function field analogue of Beilinson's conjectures is formulated in R. Sreekantan, Non-Archimedean regulator maps and special values of $L$-functions, Cy …
- 1,404