Related papers: Local vanishing for F-pure threefolds

We show that a plt surface singularity $(P\in X,B)$ is $F$-liftable if and only if it is $F$-pure and is not a rational double point of type $E_8^1$ in characteristic $p=5$. As a consequence, we prove the logarithmic extension theorem for…

Let M be a compact locally conformal hyperkaehler manifold. We prove a version of Kodaira-Nakano vanishing theorem for M. This is used to show that M admits no holomorphic differential forms, and the cohomology of the structure sheaf…

We obtain a closed form polynomial expression for certain coefficients of Drinfeld-Goss double-cuspidal modular forms which are eigenforms for the degree one Hecke operators with power eigenvalues, and we use those formulas to prove…

We prove the logarithmic extension theorem for one-forms on strongly $F$-regular singularities. Additionally, we establish the logarithmic extension theorem for one-forms on three-dimensional klt singularities in characteristic $p>41$. To…

Given a logarithmic $1$-form on the snc locus of a log canonical surface pair $(X, D)$ over a perfect field of characteristic $p \ge 7$, we show that it extends with at worst logarithmic poles to any resolution of singularities. We also…

Suppose $R$ is an excellent ring of dimension $3$ and has rational singularities. Let $\pi:X \longrightarrow \mathrm{Spec} \ R$ be a blow-up and $\phi: W \longrightarrow X$ be any projective, birational morphism such that $X$ and $W$ are…

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 prove that the homology groups of any connected reductive group over a field with coefficients in the Steinberg representation vanish in a range. The generalizes work of Ash-Putman-Sam on the classical split groups. We state a…

In this paper, we prove a Kawamata--Viehweg type vanishing theorem for smooth Fano threefolds, canonical del Pezzo surfaces and del Pezzo fibrations in positive characteristic.

Given a smooth formal scheme over the ring of integers of a mixed-characteristic perfectoid field, we study its $p$-adic vanishing cycles via de Rham--Witt and $q$-de Rham complexes.

Let k be an infinite perfect field of positive characteristic p and assume that strong resolution of singularities holds over k. We prove that, if X is a d-dimensional noetherian scheme whose underlying reduced scheme is essentially of…

We prove the Kawamata-Viehweg vanishing theorem for a large class of divisors on surfaces in positive characteristic. By using this vanishing theorem, Reider-type theorems and extension theorems of morphisms for normal surfaces are…

Bott proved a strong vanishing theorem for sheaf cohomology on projective space. It holds for toric varieties, but not for most other varieties. We prove Bott vanishing for the quintic del Pezzo surface, also known as the moduli space…

Following [Fra08, AF14] we construct Rabinowitz Floer homology for negative line bundles over symplectic manifolds and prove a vanishing result. In [Rit14] Ritter showed that symplectic homology of these spaces does not vanish, in general.…

This paper establishes a second vanishing theorem for formal local cohomology modules over Noetherian local rings. We introduce the \textit{formal dimension} invariant and characterize the vanishing of higher formal local cohomology in…

We consider compactifications of the space of triples of distinct points in projective $n$-space. One such space is a singular variety of configurations of points and lines; another is the smooth compactification of Fulton and MacPherson;…

We show that a projective variety with an int-amplified endomorphism of degree invertible in the base field satisfies Bott vanishing. This is a new way to analyze which varieties have nontrivial endomorphisms. In particular, we extend some…

We explicitly describe cohomology of the sheaf of differential forms with poles along a semiample divisor on a complete simplicial toric variety. As an application, we obtain a new vanishing theorem which is an analogue of the…

We give conceptual proofs of some well known results concerning compact non-positively curved locally symmetric spaces. We discuss vanishing and non-vanishing of Pontrjagin numbers and Euler characteristics for these locally symmetric…

Motivated by connections to intersection homology of toric morphisms, the motivic monodromy conjecture, and a question of Stanley, we study the structure of triangulations of simplices whose local h-polynomial vanishes. As a first step, we…