Related papers: Weak positivity via mixed Hodge modules

We prove that in positive characteristic a module with good filtration for a group of type E6 restricts to a module with good filtration for a subgroup of type F4. (Recall that a filtration of a module for a semisimple algebraic group is…

Theory of weak localization is developed for two-dimensional holes in the presence of in-plane magnetic field. The Zeeman splitting even in the hole momentum results in the spin-dependent phase changing the quantum interference. The…

Using the $\infty$-categorical enhancement of mixed Hodge modules constructed by the author in a previous paper, we explain how mixed Hodge modules canonically extend to algebraic stacks, together with all the $6$ operations and weights. We…

We define a filtration of a standard Whittaker module over a complex semisimple Lie algebra and and establish its fundamental properties. Our filtration specialises to the Jantzen filtration of a Verma module for a certain choice of…

We introduce the notion of filtered perversity of a filtered differential complex on a complex analytic manifold $X$, without any assumptions of coherence, with the purpose of studying the connection between the pure Hodge modules and the…

In this note we show that the irreducible twisted modules of a holomorphic, $C_2$-cofinite vertex operator algebra $V$ have $L_0$-weights at least as large as the smallest $L_0$-weight of $V$. Hence, if $V$ is of CFT-type, then the twisted…

This is partly a survey article on nonabelian Hodge theory, but we also give proofs of results that have only been announced elsewhere. In the introduction we discuss a wide range of recent work on this subject and give some references. In…

A measurement consists in coupling a system to a probe and reading the output of the probe to gather information about the system. The weaker the coupling, the smaller the back-action on the system, but also the less information conveyed.…

In this paper, we introduce the notions of Gorenstein weak injective and weak flat modules respectively in terms of weak injective and weak flat modules, which is larger than classical classes of Gorenstein injective and flat modules. In…

Let $W$ be a finite irreducible real reflection group, which is a Coxeter group. We explicitly construct a basis for the module of differential 1-forms with logarithmic poles along the Coxeter arrangement by using a primitive derivation. As…

We exhibit rationally ergodic, weakly mixing measure preserving transformations which are not subsequence rationally weakly mixing and give a condition for smoothness of renewal sequences.

We use Hodge theory to relate poles of the Archimedean zeta function $Z_f$ of a holomorphic function $f$ with several invariants of singularities. First, we prove that the largest nontrivial pole of $Z_f$ is the negative of the minimal…

We show that negative refraction in materials can occur at frequencies $\omega$ where the real parts of the permittivity $\veps(\omega)$ and the permeability $\mu(\omega)$ have different sign, and that light with such frequencies can…

We generalize positivity results due to Popa-Wu and Popa-Schnell for Hodge modules and Higgs bundles on smooth projective varieties to the case of smooth proper DM stacks admitting projective coarse moduli spaces. This paper is the first in…

In this article, we study the nature of zeros of weakly holomorphic modular forms. In particular, we prove results about transcendental zeros of modular forms of higher levels and for certain Fricke groups which extend a work of Kohnen.…

In this note we show that for analytic semigroups the so-called Weiss condition of uniform boundedness of the operators $Re(\lambda)^\einhalb C(\lambda+A)^{-1}, \qquad Re(\lambda)>0$ on the complex right half plane and weak Lebesgue…

We show that a weakly holomorphic modular function can be written as a sum of modular units of higher level. We further find a necessary and sufficient condition for a Siegel modular function of degree $g$ to have neither zero nor pole on…

Let $R$ be a commutative Noetherian ring, $\fa$ be an ideal of $R$ and $M$ be an $R$-module. The main purpose of this paper is to answer the Hartshorn's questions in the class of weakly Laskerian modules. It is shown that if $s\geq 1$ is a…

In this study, all rings are commutative with non-zero identity and all modules are considered to be unital. Let $M$ be a left $R$-module. A proper submodule $N$ of $M$ is called an $S$-$weakly$ $prime$ submodule if $0_{M}\neq f(m)\in N$…

Notions of weak and uniformly weak mixing (to zero) are defined for bounded sequences in arbitrary Banach spaces. Uniformly weak mixing for vector sequences is characterized by mean ergodic convergence properties. For bounded sequences,…