Let $R$ be a commutative Noetherian ring of prime characteristic $p$ . In this paper, we give a short proof using filter regular sequences that the set of associated prime ideals of $H_{I}^{t}(R)$ is finite for any ideal $I$ and for any $t\geqslant 0$ when $R$ has finite $F$ -representation type or finite singular locus. This extends a previous result by Takagi–Takahashi and gives affirmative answers

Ringel’s right-strongly quasi-hereditary algebras are a distinguished class of quasi-hereditary algebras of Cline–Parshall–Scott. We give characterizations of these algebras in terms of heredity chains and right rejective subcategories. We prove that any artin algebra of global dimension at most two is right-strongly quasi-hereditary. Moreover we show that the Auslander algebra of a representation-finite

Let $A$ be an expansive dilation on $\mathbb{R}^{n}$ and $\unicode[STIX]{x1D711}:\mathbb{R}^{n}\times [0,\infty )\rightarrow [0,\infty )$ an anisotropic growth function. In this article, the authors introduce the anisotropic weak Musielak–Orlicz Hardy space $\mathit{WH}_{A}^{\unicode[STIX]{x1D711}}(\mathbb{R}^{n})$ via the nontangential grand maximal function and then obtain its Littlewood–Paley characterizations

Let $s\in \mathbb{R}$ and $0

We investigate products of certain double cosets for the symmetric group and use the findings to derive some multiplication formulas for the $q$ -Schur superalgebras. This gives a combinatorialization of the relative norm approach developed in Du and Gu (A realization of the quantum supergroup $\mathbf{U}(\mathfrak{g}\mathfrak{l}_{m|n})$ , J. Algebra 404 (2014), 60–99). We then give several applications

The author gives the analytic properties of the Rankin–Selberg convolutions of two half-integral weight Maass forms in the plus space. Applications to the Koecher–Maass series associated with nonholomorphic Siegel–Eisenstein series are given.

Let $k$ be an imaginary quadratic field with $\operatorname{Cl}_{2}(k)\simeq V_{4}$ . It is known that the length of the Hilbert $2$ -class field tower is at least $2$ . Gerth (On 2-class field towers for quadratic number fields with $2$ -class group of type $(2,2)$ , Glasgow Math. J. 40(1) (1998), 63–69) calculated the density of $k$ where the length of the tower is $1$ ; that is, the maximal unramified

Let $R$ be a two-sided Noetherian ring, and let $M$ be a nilpotent $R$ -bimodule, which is finitely generated on both sides. We study Gorenstein homological properties of the tensor ring $T_{R}(M)$ . Under certain conditions, the ring $R$ is Gorenstein if and only if so is $T_{R}(M)$ . We characterize Gorenstein projective $T_{R}(M)$ -modules in terms of $R$ -modules.

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In order to work with non-Nagata rings which are Nagata “up-to-completely-decomposed-universal-homeomorphism,” specifically finite rank Hensel valuation rings, we introduce the notions of pseudo-integral closure, pseudo-normalization, and pseudo-Hensel valuation ring. We use this notion to give a shorter and more direct proof that $H_{\operatorname{cdh}}^{n}(X,F_{\operatorname{cdh}})=H_{l\operatorname{dh}}^{n}(X

We will establish a nearby and vanishing cycle formalism for the arithmetic $\mathscr{D}$ -module theory following Beilinson’s philosophy. As an application, we define smooth objects in the framework of arithmetic $\mathscr{D}$ -modules whose category is equivalent to the category of overconvergent isocrystals.

We give a sufficient condition for the hypergeometric function $_{3}F_{2}$ to be a linear combination of the logarithm of algebraic functions.

For a certain class of hypergeometric functions $_{3}F_{2}$ with rational parameters, we give a sufficient condition for the special value at $1$ to be expressed in terms of logarithms of algebraic numbers. We give two proofs, both of which are algebro-geometric and related to higher regulators.

We discuss the kernel of the localization map from étale motivic cohomology of a variety over a number field to étale motivic cohomology of the base change to its completions. This generalizes the Hasse principle for the Brauer group, and is related to Tate–Shafarevich groups of abelian varieties.

In this paper, we construct Chern classes from the relative $K$ -theory of modulus pairs to the relative motivic cohomology defined by Binda–Saito. An application to relative motivic cohomology of henselian dvr is given.

For a character of the absolute Galois group of a complete discrete valuation field, we define a lifting of the refined Swan conductor, using higher dimensional class field theory.

We use higher ideles and duality theorems to develop a universal approach to higher dimensional class field theory.

This paper examines Euler characteristics and characteristic classes in the motivic setting. We establish a motivic version of the Becker–Gottlieb transfer, generalizing a construction of Hoyois. Making calculations of the Euler characteristic of the scheme of maximal tori in a reductive group, we prove a generalized splitting principle for the reduction from $\operatorname{GL}_{n}$ or $\operatorname{SL}_{n}$

In this paper, we construct surfaces in $\mathbf{P}^{3}$ with large higher Chow groups defined over a Laurent power series field. Explicit elements in higher Chow group are constructed using configurations of lines contained in the surfaces. To prove the independentness, we compute the extension class in the Galois cohomologies by comparing them with the classical monodromies. It is reduced to the

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