11
votes
Accepted
An unpublished note by Bloch-Kato on p-divisible groups and Dieudonné crystals
The unpublished note was no longer on the Web (also archive.org did not have it cached). I asked professor Moonen for a copy to share with you, here it is: p-divisible groups and Dieudonné crystals by ...
- 188k
7
votes
Accepted
$p$-adic Kato--Nakayama space
I believe many people have thought about this at some point, and I don't think such a construction is known.
In the paper https://arxiv.org/abs/1207.3380 , Yves Andre considers the real blowups (in ...
- 16.1k
5
votes
A log structure on the moduli space of curves
As Piotr Achinger suggested in a comment, your log moduli space is the direct product of $M_{g,n}$ with the log point $\operatorname{Spec}(\mathbb{N}^n \to \mathbb{C})$ given by the monoid map $(x_1,\...
- 45.7k
4
votes
Intersection complex of genus-zero curves?
Not a complete answer, too long for a comment. I think you'd find it useful to think about these things in terms of Hassett's moduli spaces of weighted pointed curves. Here's the brief version. Fix a ...
- 40.2k
4
votes
A log structure on the moduli space of curves
(I'm not sure this is a real answer, but it was too long for a comment)
I've never seen the log structure you consider.
By "log moduli space of (stable) log curves" usually one refers to the natural ...
- 1,030
3
votes
Reference request: Kummer étale topology and tame topology
He did not say that the sites are equal as this claim is wrong in general, but that the categories of covers, i.e. finite morphisms which cover the log scheme (See definition 3.1. of the same paper), ...
3
votes
Is $(x^2y,xy^2)$ log smooth?
Warning: I'm not an expert on logarithmic geometry.
According to Proposition 4.1.2. of Ogus' Lectures on Logarithmic Algebraic Geometry, a log smooth morphism (of fine log schemes) is log flat. Log ...
- 3,079
2
votes
Accepted
Reference request for log-differential forms
Do the proofs of Theorem IV.1.2.4 and Proposition IV.1.2.11 in Ogus' book ``Lectures on Logarithmic Algebraic Geometry'' help?
- 9,263
2
votes
Accepted
Understanding the picture of monoidal space
Ogus states that he draws a log scheme $(X,\mathcal{M})$ by first drawing $X$ and then adding a picture of $\operatorname{Spec}\mathcal{M}_x$ at each $x\in X.$ (He says this on page 21.)
In this case, ...
- 1,349
2
votes
Properties of log smooth schemes
TL;DR the answer is no, but yes if(f) the morphism is saturated.
Notation: $\mathbf{A}_P = {\rm Spec}(k[P])$ with the standard log structure.
Basic counterexample. Let $n$ be an integer invertible ...
- 16.1k
1
vote
Accepted
Locally toric resolutions of compactifications
I am just posting my second comment as an answer. I now understand that the equivalence relation of "toric-equivalence" is the smallest equivalence relation generated by the "toric type" relation, ...
1
vote
What are Log Stacks
$\DeclareMathOperator\Log{Log}$From Gilliam - Logarithmic stacks and minimality:
A category fibered in groupoids (CFG) over schemes with a map to Olsson's stack $\Log$ induces a CFG over log schemes. ...
- 1,094
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