Yuya Matsumoto

Yuya Matsumoto
Tokyo University of Science | TUS

About

16
Publications
370
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96
Citations
Citations since 2016
13 Research Items
85 Citations
2016201720182019202020212022051015
2016201720182019202020212022051015
2016201720182019202020212022051015
2016201720182019202020212022051015

Publications

Publications (16)
Article
We consider μ p \mu _p - and α p \alpha _p -actions on RDP K3 surfaces (K3 surfaces with rational double point (RDP) singularities allowed) in characteristic p > 0 p > 0 . We study possible characteristics, quotient surfaces, and quotient singularities. It turns out that these properties of μ p \mu _p - and α p \alpha _p -actions are analogous to t...
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We study torsors under finite group schemes over the punctured spectrum of a singularity $x\in X$ in positive characteristic. We show that the Dieudonn\'e module of the (loc,loc)-part $\mathrm{Picloc}^{\mathrm{loc},\mathrm{loc}}_{X/k}$ of the local Picard sheaf can be described in terms of local Witt vector cohomology, making $\mathrm{Picloc}^{\mat...
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We study isolated quotient singularities by finite and linearly reductive group schemes (lrq singularities for short) and show that they satisfy many, but not all, of the known properties of finite quotient singularities in characteristic zero: (1) From the lrq singularity we can recover the group scheme and the quotient presentation. (2) We establ...
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We classify purely inseparable morphisms of degree $p$ between rational double points (RDPs) in characteristic $p$. Using such morphisms, we show that any RDP admit a finite smooth covering.
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We give lower bounds of, or moreover determine, the height of K3 surfaces in characteristic $p$ admitting non-taut rational double point singularities or actions of local group schemes of order $p$ ($\mu_p$ or $\alpha_p$). The proof is based on the computation of the pullback maps by inseparable morphisms, such as Frobenius, on certain $W_n$-valued...
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Consider the canonical ($\mu_2$- or $\alpha_2$-) covering of a classical or supersingular Enriques surface in characteristic $2$. Assuming that it has only rational double points as singularities, we determine all possible configurations of singularities on it, in both classical and supersingular cases.
Preprint
We consider $\mu_p$- and $\alpha_p$-actions on RDP K3 surfaces (K3 surfaces with rational double point singularities allowed) in characteristic $p > 0$. We study possible characteristic, quotient surfaces, and quotient singularities. It turns out that these properties of $\mu_p$- and $\alpha_p$-actions are analogous to those of $\mathbb{Z}/l\mathbb...
Article
Full-text available
In characteristic $0$, symplectic automorphisms of K3 surfaces (i.e. automorphisms preserving the global $2$-form) and non-symplectic ones behave differently. In this paper we consider the actions of the group scheme $\mu_{n}$ on K3 surfaces (with rational double point singularities) in characteristic $p$, where $n$ may be divisible by $p$. After i...
Article
Consider an arbitrary automorphism of an Enriques surface with its lift to the covering K3 surface. We prove a bound of the order of the lift acting on the anti-invariant cohomology sublattice of the Enriques involution. We use it to obtain some mod 2 constraint on the original automorphism. As an application, we give a necessary condition for Sale...
Article
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We prove that a K3 surface with an automorphism acting on the global $2$-forms by a primitive $m$-th root of unity does not degenerate if $m \neq 1,2,3,4,6$ (assuming the existence of the so-called Kulikov models). To prove this we study the rationality of the actions of automorphisms on the graded quotients of the weight filtration of the $l$-adic...
Article
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A K3 surface $X$ over a $p$-adic field $K$ is said to have good reduction if it admits a proper smooth model over the integer ring of $K$. Assuming this, we say that a subgroup $G$ of $\mathrm{Aut}(X)$ is extendable if $X$ admits a proper smooth model equipped with $G$-action (compatible with the action on $X$). We show that $G$ is extendable if it...
Article
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We show that an unramified Galois-action on second $\ell$-adic cohomology of a K3 surface over a p-adic field implies that the surface has good reduction after a finite and unramified extension. We give examples where this unramified extension is really needed. Moreover, we give applications to good reduction after tame extensions and Kuga-Satake A...
Article
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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 abelia...
Article
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...

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