Perfectoid signature, perfectoid Hilbert-Kunz multiplicity, and an application to local fundamental groups
We define a (perfectoid) mixed characteristic version of $ F $-signature and Hilbert-Kunz
multiplicity by utilizing the perfectoidization functor of Bhatt-Scholze and Faltings' normalized …
multiplicity by utilizing the perfectoidization functor of Bhatt-Scholze and Faltings' normalized …
Linearly reductive quotient singularities
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 …
singularities for short) and show that they satisfy many, but not all, of the known properties of …
Uniform bounds on symbolic powers in regular rings
T Murayama - arXiv preprint arXiv:2111.06049, 2021 - arxiv.org
We prove a uniform bound on the growth of symbolic powers of arbitrary (not necessarily
radical) ideals in arbitrary (not necessarily excellent) regular rings of all characteristics. This …
radical) ideals in arbitrary (not necessarily excellent) regular rings of all characteristics. This …
Global generation of test ideals in mixed characteristic and applications
Suppose that $ X $ is an integral scheme (quasi-) projective over a complete local ring of
mixed characteristic. Using ideas of Takamatsu-Yoshikawa and Bhatt-Ma-et. al, we define a …
mixed characteristic. Using ideas of Takamatsu-Yoshikawa and Bhatt-Ma-et. al, we define a …
General hyperplane sections of log canonical threefolds in positive characteristic
K Sato - arXiv preprint arXiv:2303.14599, 2023 - arxiv.org
In this paper, we prove that if a $3 $-dimensional quasi-projective variety $ X $ over an
algebraically closed field of characteristic $ p> 3$ has only log canonical singularities, then …
algebraically closed field of characteristic $ p> 3$ has only log canonical singularities, then …
Big Cohen–Macaulay Test Ideals in Equal Characteristic Zero Via Ultraproducts
T Yamaguchi - Nagoya Mathematical Journal, 2023 - cambridge.org
BIG COHEN–MACAULAY TEST IDEALS IN EQUAL CHARACTERISTIC ZERO VIA
ULTRAPRODUCTS Page 1 Nagoya Math. J., 251 (2023), 549–575 DOI 10.1017/nmj.2022.41 …
ULTRAPRODUCTS Page 1 Nagoya Math. J., 251 (2023), 549–575 DOI 10.1017/nmj.2022.41 …
Deformations of log terminal and semi log canonical singularities
K Sato, S Takagi - Forum of Mathematics, Sigma, 2023 - cambridge.org
In this paper, we prove that klt singularities are invariant under deformations if the generic
fiber is-Gorenstein. We also obtain a similar result for slc singularities. These are …
fiber is-Gorenstein. We also obtain a similar result for slc singularities. These are …
Arithmetic and geometric deformations of threefolds
F Bernasconi, I Brivio, S Filipazzi - Bulletin of the London …, 2024 - Wiley Online Library
We show that mixed‐characteristic and equi‐characteristic small deformations of 3‐
dimensional canonical (resp., terminal) singularities with perfect residue field of …
dimensional canonical (resp., terminal) singularities with perfect residue field of …
Closure-theoretic proofs of uniform bounds on symbolic powers in regular rings
T Murayama - arXiv preprint arXiv:2205.01153, 2022 - arxiv.org
We give short, closure-theoretic proofs for uniform bounds on the growth of symbolic powers
of ideals in regular rings. The author recently proved these bounds in mixed characteristic …
of ideals in regular rings. The author recently proved these bounds in mixed characteristic …
Torsors over the Rational Double Points in Characteristic
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 …
x\in X $ in positive characteristic. We show that the Dieudonn\'e module of the (loc, loc)-part …