Kazuhiro Ito

Kazuhiro Ito
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Mathematics - Algebraic Geometry (3)
 
Mathematics - Number Theory (3)

Publications Authored By Kazuhiro Ito

For a K3 surface over a field of characteristic 2 which is finitely generated over its prime subfield, we prove that the cokernel of the natural map from the Brauer group of the base field to that of the K3 surface is finite modulo the 2-primary torsion subgroup. In characteristic different from 2, such results were previously proved by A. N. Read More

We give an unconditional construction of K3 surfaces over finite fields with given L-function, up to finite extensions of the base fields, under some mild restrictions on the characteristic. Previously, such results were obtained by Taelman assuming semistable reduction. The main contribution of this paper is to make Taelman's proof unconditional. Read More

We focus on non-isotrivial families of $K3$ surfaces in positive characteristic $p$ whose geometric generic fibers satisfy $\rho \geq 21-2h$ and $h \geq 3$, where $\rho$ is the Picard number and $h$ is the height of the formal Brauer group. We show that, under a mild assumption on the characteristic of the base field, they have potentially supersingular reduction. Our methods depend on Maulik's results on moduli spaces of $K3$ surfaces and the construction of sections of powers of Hodge bundles due to van der Geer and Katsura. Read More