14 citations · 85 across the 21 of their papers we have counts for
23 papers
Equidimensional morphisms onto splinters are pure
Takumi Murayama
We prove that a Noetherian ring is a splinter if and only if for every equidimensional surjective morphism , the map $R \to S…
Finiteness of associated primes for local cohomology modules of excellent locally unramified regular rings of finite Krull dimension
Takumi Murayama
Thirty years ago, Huneke (for local rings) and Lyubeznik (in general) conjectured that for all regular rings , the local cohomology modules have finitely many associa…
Moving Seshadri constants and effective Fujita-type conjectures
Takumi Murayama
Fujita's conjecture is known to be false in positive characteristic. We conjecture and give an approach to a new variant of Fujita's conjecture for the basepoint-freeness, very amp…
Injectivity theorems and cubical descent for schemes, stacks, and analytic spaces
Takumi Murayama
We prove relative injectivity, torsion-freeness, and vanishing theorems for generalized normal crossing pairs on schemes, algebraic stacks, formal schemes, semianalytic germs of co…
The relative minimal model program for excellent algebraic spaces and analytic spaces in equal characteristic zero
Shiji Lyu, Takumi Murayama
We establish the relative minimal model program with scaling for locally projective morphisms of quasi-excellent algebraic spaces admitting dualizing complexes, quasi-excellent for…
Pure subrings of Du Bois singularities are Du Bois singularities
Charles Godfrey, Takumi Murayama
Let be a cyclically pure map of Noetherian -algebras. In this paper, we show that if has Du Bois singularities, then has Du Bois singularities. Our re…
Closure-theoretic proofs of uniform bounds on symbolic powers in regular rings
Takumi Murayama
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 characteris…
Variants of normality and steadfastness deform
Alexander Bauman, Havi Ellers, Gary Hu +3
The cancellation problem asks whether implies . Hamann introduced the class of steadfast rings as the rings for which…
Rational linear subspaces of hypersurfaces over finite fields
María Inés de Frutos Fernández, Sumita Garai, Kelly Isham +2
Let be a hypersurface of degree defined over a finite field of characteristic . We prove that if , then contains…
Uniform bounds on symbolic powers in regular rings
Takumi Murayama
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 characteristic…
New constructions of nef classes on self-products of curves
Mihai Fulger, Takumi Murayama
We study the nef cone of self-products of a curve. When the curve is very general of genus , we construct a nontrivial class of self-intersection 0 on the boundary of the nef…
Relative vanishing theorems for -schemes
Takumi Murayama
We prove the relative Grauert-Riemenschneider vanishing, Kawamata-Viehweg vanishing, and Kollár injectivity theorems for proper morphisms of schemes of equal characteristic zero, s…
Excellence, F-singularities, and solidity
Rankeya Datta, Takumi Murayama, Karen E. Smith
An -algebra is -solid if there exists a nonzero -linear map . In characteristic , the study of -singularities such as Frobenius splittings impli…
A uniform treatment of Grothendieck's localization problem
Takumi Murayama
Let be a proper flat morphism of locally noetherian schemes. Then, the locus in over which is smooth is stable under generization. We prove that under sui…
Tate algebras and Frobenius non-splitting of excellent regular rings
Rankeya Datta, Takumi Murayama
An excellent ring of prime characteristic for which the Frobenius map is pure is also Frobenius split in many commonly occurring situations in positive characteristic commutative a…
Permanence properties of -injectivity
Rankeya Datta, Takumi Murayama
We prove that -injectivity localizes, descends under faithfully flat homomorphisms, and ascends under flat homomorphisms with Cohen-Macaulay and geometrically -injective fibe…
Seshadri Constants and Fujita's Conjecture via Positive Characteristic Methods
Takumi Murayama
In 1988, Fujita conjectured that there is an effective and uniform way to turn an ample line bundle on a smooth projective variety into a globally generated or very ample line bund…
Seshadri constants for vector bundles
Mihai Fulger, Takumi Murayama
We introduce Seshadri constants for line bundles in a relative setting. They generalize the classical Seshadri constants of line bundles on projective varieties and their extension…
The gamma construction and asymptotic invariants of line bundles over arbitrary fields
Takumi Murayama
We extend results on asymptotic invariants of line bundles on complex projective varieties to projective varieties over arbitrary fields. To do so over imperfect fields, we prove a…
Effective generation and twisted weak positivity of direct images
Yajnaseni Dutta, Takumi Murayama
In this paper, we study pushforwards of log pluricanonical bundles on projective log canonical pairs over the complex numbers, partially answering a Fujita-type conjecture…
Frobenius-Seshadri constants and characterizations of projective space
Takumi Murayama
We introduce higher-order variants of the Frobenius-Seshadri constant due to Mustaţă and Schwede, which are defined for ample line bundles in positive characteristic. These constan…
Dilated Floor Functions That Commute
Jeffrey C. Lagarias, Takumi Murayama, D. Harry Richman
We determine all pairs of real numbers such that the dilated floor functions and commute under composition, i.e., such that $\lfloo…
Robust Graph Ideals
Adam Boocher, Bryan Christopher Brown, Timothy Duff +4
Let I be a toric ideal. We say I is robust if its universal Groebner basis is a minimal generating set. We show that any robust toric ideal arising from a graph G is also minimally…