An analog to Deuring's criterion for good reduction of elliptic curves

On the Deuring Polynomial for Drinfeld Modules in Legendre Form

We study a family $ψ^λ$ of $\mathbb F_q[T]$-Drinfeld modules, which is a natural analog of Legendre elliptic curves. We then find a surprising recurrence giving the corresponding Deuring polynomial $H_{p(T)}(λ)$ characterising supersingular Legendre Drinfeld modules $ψ^λ$ in characteristic $p(T)$.

Cut-by-curves criterion for the log extendability of overconvergent isocrystals

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 crossing divisor, under certain assumption. This is a $p$-adic analogue of a version of cut-by-curves criterion for regular singuarity of an integrable connection on a smooth variety over a field of characteristic 0. In the course of the proof, we also prove a kind of cut-by-curves criteria on solvability, highest ramification break and exponent of $\nabla$-modul…

Good reduction criterion for K3 surfaces

We prove a Neron--Ogg--Shafarevich type criterion for good reduction of K3 surfaces, which states that a K3 surface over a complete discrete valuation field has potential good reduction if its $l$-adic cohomology group is unramified. We also prove a $p$-adic version of the criterion. (These are analogues of the criteria for good reduction of abelian varieties.) The model of the surface will be in general not a scheme but an algebraic space. As a corollary of the criterion we obtain the surjectivity of the period map of K3 surfaces in positive characteristic.

On good reduction of some K3 surfaces related to abelian surfaces

The Neron--Ogg--Safarevic criterion for abelian varieties tells that whether an abelian variety has good reduction or not can be determined from the Galois action on its l-adic etale cohomology. We prove an analogue of this criterion for some special kind of K3 surfaces (those which admit Shioda--Inose structures of product type), which are deeply related to abelian surfaces. We also prove a p-adic analogue. This paper includes Ito's unpublished result for Kummer surfaces.

不来自阿贝尔簇的局部系统

Local systems which do not come from abelian varieties

针对有限域上光滑曲线，通过证明受特征零霍奇理论判别启发的阿贝尔簇局部系统必满足的准则，构造出穿孔后具有几何起源却不来自阿贝尔簇族的局部系统。

K3曲面的内龙-奥格-沙法列维奇准则

A Néron-Ogg-Shafarevich criterion for K3 surfaces

本文针对K3曲面修正了内龙-奥格-沙法列维奇准则，在潜在半稳定约化假设下给出K3曲面具有好约化的等价条件，并证明了p进平展上同调的对应结果。