Kazuma Shimomoto

Almost Cohen-Macaulay and almost regular algebras via almost flat extensions

The present paper deals with various aspects of the notion of almost Cohen-Macaulay property, which was introduced and studied by Roberts, Singh and Srinivas. We employ the definition of almost zero modules as defined by a value map, which is different from the version of Gabber-Ramero. We prove that, if the local cohomology modules of an algebra

Local cohomology of Du Bois singularities and applications to families

T

BERTINI THEOREM FOR NORMALITY ON LOCAL RINGS IN MIXED CHARACTERISTIC (APPLICATIONS TO CHARACTERISTIC IDEALS)

of certain type over a local Noetherian ring are almost zero,

THE FROBENIUS ACTION ON LOCAL COHOMOLOGY MODULES IN MIXED CHARACTERISTIC

T

Integral perfectoid big Cohen–Macaulay algebras via André’s theorem

maps to a big Cohen-Macaulay algebra. Then we study how the almost Cohen-Macaulay property behaves under almost faithfully flat extension. As a consequence, we study the structure of

On the Witt Vectors of Perfect Rings in Positive Characteristic

F

Specialization method in Krull dimension two and Euler system theory over normal deformation rings

-coherent rings of positive characteristic in terms of almost regularity.

On the semicontinuity problem of fibers and global F-regularity

In this paper we study the local cohomology modules of Du Bois singularities. Let

An application of the almost purity theorem to the homological conjectures

(R,m)

On the upper semi-continuity of the Hilbert–Kunz multiplicity

be a local ring, we prove that if