Related papers: Log smoothness and polystability over valuation ri…

By works of Kedlaya and Shiho, it is known that, for a smooth variety $\overline{X}$ over a field of positive characteristic and its simple normal crossing divisor $Z$, an overconvergent isocrystal on the compliment of $Z$ satisfying a…

A map of fine log schemes $X \to Y$ induces a map from the scheme underlying $X$ to Olsson's algebraic stack of strict morphisms of fine log schemes over $Y$. A sheaf on $X$ is called \emph{log flat over} $Y$ iff it is flat over this…

We give sufficient conditions for cohomological flatness (in dimension 0) over discrete valuation rings, generalizing classical results of Raynaud in two different ways. The first is a higher dimensional generalization of Raynaud's…

We complete our proof that given an overconvergent F-isocrystal on a variety over a field of positive characteristic, one can pull back along a suitable generically finite cover to obtain an isocrystal which extends, with logarithmic…

Let X be a smooth variety over a field of positive characteristic, and let E be an overconvergent isocrystal on X. We establish a criterion for the existence of a "canonical logarithmic extension" of E to a good compactification of X. In…

We prove that a projective vertical exact log smooth morphism of fs log analytic spaces with a base of log rank one yields polarized log Hodge structures in the canonical way.

In this paper, we establish a criterion for an overconvergent isocrystal on a smooth variety over a field of characteristic $p>0$ to extend logarithmically to its smooth compactification whose complement is a strict normal crossing divisor.…

We study several rigidity properties of $p$-adic local systems on a smooth rigid analytic space $X$ over a $p$-adic field. We prove that the monodromy of the log isocrystal attached to a $p$-adic local system is ''rigid'' along irreducible…

We consider the stack $\mathcal{L}og_X$ parametrizing log schemes over a log scheme $X$, and weak and strong properties of log morphisms via $\mathcal{L}og_X$, as defined by Olsson. We give a concrete combinatorial presentation of…

Let $f : X \rightarrow Y$ be a dominant generically smooth morphism between irreducible smooth projective curves over an algebraically closed field $k$ such that ${\rm Char}(k)> \text{degree}(f)$ if the characteristic of $k$ is nonzero. We…

Stable surfaces and their log analogues are the type of varieties naturally occuring as boundary points in moduli spaces. We extend classical results of Kodaira and Bombieri to this more general setting: if $(X,\Delta)$ is a stable log…

In this paper, we prove a `cut-by-curves criterion' for an overconvergent isocrystal on a smooth variety over a field of characteristic $p>0$ to extend logarithmically to its smooth compactification whose complement is a strict normal…

In this short notes, we prove a stronger version of Theorem 0.6 in our previous paper arXiv:1709.01485: Given a smooth log scheme $(\mathcal{X} \supset \mathcal{D})_{W(\mathbb{F}_q)}$, each stable twisted $f$-periodic logarithmic Higgs…

Let $(X,L)$ be a polarized smooth projective variety. For any basepoint-free linear system $\mathcal{L}_{V}$ with $V\subset H^{0}(X,\mathcal{O}_{X}(L))$ we consider the syzygy bundle $M_{V}$ as the kernel of the evaluation map $V\otimes…

Let V be a complete discrete valuation ring of unequal characteristic with perfect residue field. Let X be smooth separated formal V-scheme, Z a strict normal crossing divisor of X and T a divisor of the special fiber of X. We study in this…

We characterise when the log arc scheme of a fine log scheme $(X, M)$, with $X$ a variety over a field of characteristic zero, is irreducible. This generalises the theorem of Kolchin that the (ordinary) arc scheme of $X$ is irreducible…

Let $R$ be a complete discrete valuation ring with fraction field of characteristic $0$ and algebraically closed residue field of characteristic $p>0$. Let $X_R \to \mathrm{Spec}(R)$ be a smooth projective morphism of relative dimension…

Let X be a separated finite type scheme over a noetherian base ring K. There is a complex C(X) of topological O_X-modules on X, called the complete Hochschild chain complex of X. To any O_X-module M - not necessarily quasi-coherent - we…

Let $\mathcal{V}$ be a mixed characteristic complete discrete valuation ring, $k$ its residual field, $\mathcal{P}$ a proper smooth formal scheme over $\mathcal{V}$, $P$ its special fiber, $T$ a divisor of $P$, $U:=P\setminus T$, $Y$ a…

Recent work ([18], [1]) has produced a complete list of weighted homogeneous surface singularities admitting smoothings whose Milnor fibre has only trivial rational homology (a "rational homology disk"). Though these special singularities…