Related papers: A New Subadditivity Formula for Test Ideals

We give new proofs for many injectivity results in analysis that make more careful use of the duality between unital abelian C*-algebras and compact Hausdorff spaces. We then extend many of these results to incorporate group actions. Our…

Classical variational Hodge structure theory characterizes the algebraicity of Hodge classes by studying the transversality of period mappings under geometric deformations. However, when algebraic varieties lack appropriate deformation…

A duality theorem for the singularity category of a finite dimensional Gorenstein algebra is proved. It complements a duality on the category of perfect complexes, discovered by Happel. One of its consequences is an analogue of Serre…

Let G be a reductive algebraic group and H a closed subgroup of G. Explicit constructions of G-invariant ideals in the algebra K[G/H] are given. This allows to obtain an elementary proof of Matsushima's criterion: a homogeneous space G/H is…

We show that the Verdier quotients can be realized as subfactors by the homotopy theory of additive categories with suspensions developed in \cite{ZWLi2, ZWLi3}. As applications, we develop the homotopy theory of Nakaoka twin cotorsion…

We propose a formulation of the Equivariant Tamagawa Number Conjecture for modular motives with coefficients in universal deformation rings and Hecke algebras; something which seems to have been heretofore missing because the complexes of…

Following a method introduced by Thomas-Vasquez and developed by Grundman, we prove that many Hilbert modular threefolds of arithmetic genus $0$ and $1$ are of general type, and that some are of nonnegative Kodaira dimension. The new…

We give a combinatorial algorithm for equivariant embedded resolution of singularities of a toric variety defined over a perfect field. The algorithm is realized by a finite succession of blowings-up with smooth invariant centres that…

We introduce and evaluate a new class of hypothesis testing procedures for moment structures. The methods are valid under weak assumptions and includes the well-known Satorra-Bentler adjustment as a special case. The proposed procedures…

We give an overview of recent developments around a characteristic class version of the Hodge index theorem for singular complex algebraic varieties. This was formulated by Brasselet-Schuermann-Yokura as a conjecture expressing the…

Let $\mathfrak{g}$ be a finite-dimensional semisimple complex Lie algebra and $\theta$ an involutive automorphism of $\mathfrak{g}$. According to G. Letzter, S. Kolb and M. Balagovi\'c the fixed-point subalgebra $\mathfrak{k} =…

Let X be a smooth real algebraic variety. Let $\xi$ be a distribution on it. One can define the singular support of $\xi$ to be the singular support of the $D_X$-module generated by $\xi$ (some times it is also called the characteristic…

We present a countably infinite number of new explicit co-homogeneity one Sasaki-Einstein metrics on S^2 x S^3, in both the quasi-regular and irregular classes. These give rise to new solutions of type IIB supergravity which are expected to…

We introduce a new method to construct 4-dimensional Artin-Schelter regular algebras as normal extensions of (not necessarily noetherian) 3-dimensional ones. The method produces large classes of new 4-dimensional Artin-Schelter regular…

We prove the relative Grauert-Riemenschneider vanishing, Kawamata-Viehweg vanishing, and Koll\'ar injectivity theorems for proper morphisms of schemes of equal characteristic zero, solving conjectures of Boutot and Kawakita. Our proof uses…

We give a characterization of extremal irreducible discrete subfactors $(N\subseteq M, E)$ where $N$ is type ${\rm II}_1$ in terms of connected W*-algebra objects in rigid C*-tensor categories. We prove an equivalence of categories where…

In this paper, we prove the following differential analog of the Noether normalization lemma: for every $d$-dimensional differential algebraic variety over differentially closed field of zero characteristic there exists a surjective map…

Exact categories are a natural generalisation of abelian categories and provide a fertile ground to develop relative homological algebra. In this paper, starting from a class of relative Gorenstein projective objects in an exact category…

We formulate and establish a generalization of Koll\'ar's injectivity theorem for adjoint bundles twisted by suitable multiplier ideal sheaves. As applications, we generalize Koll\'ar's torsion-freeness, Koll\'ar's vanishing theorem, and a…

Buan, Iyama, Reiten and Smith proved that cluster-tilting objects in triangulated 2-Calabi--Yau categories are closely connected with mutation of quivers with potentials over an algebraically closed field. We prove a more general statement…