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seen Dec 10 at 1:30

Jul
2
awarded  Curious
Dec
5
revised Deformation over small disk and deformation over complex disk
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Nov
20
comment Semistable minimal model of a $K3$-surface and the special fibre
Is is true that if we have a semi-stable minimal model $X\rightarrow \mathop{spec}(R)$ with $R$ a complete discreat valuation ring, with smooth generic fibre a $K3$-surface, then the special fibre $X_0$ (with the induced log structure) is a simple normal crossing Log $K3$-surface? Even if we assume that the special fibre is reduced and that its components are geometrically irreducible why is it $d$-semistable and why $H^1(X_0,\mathcal O_{X_0}) = 0$ and $\Omega_{X_0}^2(log) = \mathcal{O}_{X_0}$?
Nov
20
comment Semistable minimal model of a $K3$-surface and the special fibre
Yes, I have seen that paper. He works on characteristic $p$ and I am on mixed characteristic. Looking at Maulik's arguments on section 4, he claims that having a semi-stable minimal model, then indeed the special fibre is combinatorial, however there is something that I am missing: He said that this follows by Nakkajima, but for Nakkajima we need to have that the special fibre to be a simple normal crossing log K3-surface. Why is it true in Maulik's paper?
Nov
18
revised Semistable minimal model of a $K3$-surface and the special fibre
added 198 characters in body; edited tags
Nov
18
comment Semistable minimal model of a $K3$-surface and the special fibre
ups… that is right!
Nov
18
asked Semistable minimal model of a $K3$-surface and the special fibre
Oct
14
comment Deformation over small disk and deformation over complex disk
I just change it. I hope it makes more sense now. Thanks.
Oct
14
revised Deformation over small disk and deformation over complex disk
deleted 157 characters in body
Oct
12
comment Deformation over small disk and deformation over complex disk
You are right Marguax. This is not the condition I want. I will modify (correct) my question tomorrow on my computer. Thanks.
Oct
12
comment Deformation over small disk and deformation over complex disk
Yes it is smooth outside the central fibre. I will take a look of SGA 1 to see if this is what I was looking for. Thanks.
Oct
12
comment Deformation over small disk and deformation over complex disk
By $X(\mathbb C)$ we understand the $\mathbb C$ points of $X$. We can give to it a structure of complex analytic space. So indeed $X_{an}=X(\mathbb C)$.
Oct
10
asked Deformation over small disk and deformation over complex disk
Aug
7
accepted Existence of logarithmic structures and d-semistability
Aug
7
asked Existence of logarithmic structures and d-semistability
Aug
5
revised Torelli-like theorem for K3 surfaces on terms of its étale cohomology
edited title
Aug
5
comment Torelli-like theorem for K3 surfaces on terms of its étale cohomology
I meant $H^2_{et}(X,\mathbb Z_p)$ on my previews comment.
Aug
5
comment Minimal semistable model for K3-surfaces.
Your are right.
Aug
5
comment Torelli-like theorem for K3 surfaces on terms of its étale cohomology
Thanks Matt. This paper of Ogus is good reference! I agree that the result may not be true just as I stayed. What I am looking for is a characterization of K3-surfaces in terms of its p-adic representations. If we Tensor $H^2(X,\mathbb Z)$ with $B_{dR}$ or $B_{HT}$ or $B_{st}$ etc.. we get different extra structures (Like Frobenius, monodromy, Filtrations etc…). It may not exist a result, but I was wondering if we can get something asking a morphism to preserve filtrations, or Frobenius or any of the extra structures we get after tensor with Fontain's rings.
Aug
3
revised Torelli-like theorem for K3 surfaces on terms of its étale cohomology
added 7 characters in body