Related papers: Variation on Artin's vanishing theorem

We prove that there exists a nonzero holderian real-to-real function vanishing together with its M. Rietz potential in all points of some set of positive length. This result improves the one of D. Beliaev and V. Havin. We also extend the…

Let $p$ be a fixed odd prime. Let $E$ be an elliptic curve defined over a number field with either good ordinary reduction or multiplicative reduction at each prime of $F$ above $p$. We shall study the characteristic element of the Selmer…

Riemann Existence Theorems for Galois covers of Mumford curves by Mumford curves are stated and proven. As an application, all finite groups are realised as full automorphism groups of Mumford curves in characteristic zero.

We use multiplication maps to give a characteristic-free approach to vanishing theorems on toric varieties. Our approach is very elementary but is enough powerful to prove vanishing theorems.

This note contains a complete proof of the Abhyankar-Moh-Suzuki theorem (in characteristic zero case).

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…

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…

We study the negative $K$-theory of singular varieties over a field of positive characteristic and in particular, prove the vanishing of $K_i(X)$ for $i < -d-2$ for a $k$-variety of dimension $d$.

Assuming the existence of a Landau-Siegel zero, we establish an explicit Deuring-Heilbronn zero repulsion phenomenon for Dirichlet $L$-functions modulo $q$. Our estimate is uniform in the entire critical strip, and improves over the…

We study a notion of derived foliations on schemes and derived schemes of arbitrary characteristics. We introduce the Hodge filtration associated to a derived foliation, which functorialy filters derived de Rham cohomology. We use this…

We show how a theorem of Gabber on alterations can be used to apply work of Cisinski, Suslin, Voevodsky, and Weibel to prove that $K_n(X)[1/p] = 0$ for $n < - \dim X$ where $X$ is a quasi-excellent noetherian scheme, $p$ is a prime that is…

Eigenvalue problems for semidefinite operators with infinite dimensional kernels appear for instance in electromagnetics. Variational discretizations with edge elements have long been analyzed in terms of a discrete compactness property. As…

We consider the decision problem of whether a particular Gromov--Witten invariant on a partial flag variety is zero. We prove that for the $3$-pointed, genus zero invariants, this problem is in the complexity class ${\sf AM}$ assuming the…

We give a necessary and sufficient condition for the existence of a local solution of the inverse problem of calculus of variations in terms of the identical vanishing of the variation of a functional on an extended space (with the number…

Abstract. In this work we derive a sufficient condition to ensure certain genus 0 entire function that can have only negative zeros. We also apply this result to the Riemann hypothesis and generalized Riemann hypothesis for some primitive…

A proof based on reduction to finite fields of Esnault-Viehweg's stronger version of Sommese Vanishing Theorem for $k$-ample line bundles is given. This result is used to give different proofs of isotriviality results of A. Parshin and L.…

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

We study vanishing theorems of tautological bundles in the sense of Berget--Eur--Spink--Tseng restricted to wonderful varieties. As an application, we prove a characteristic-independent analogue of Brieskorn's result on cohomology of…

We prove a generic vanishing type statement in positive characteristic and apply it to prove positive characteristic versions of Kawamata's theorems: a characterization of smooth varieties birational to ordinary abelian varieties and the…

We classify finite non-solvable groups with a faithful primitive irreducible complex character that vanishes on a unique conjugacy class. Our results answer a question of Dixon and Rahnamai Barghi and suggest an extension of Burnside's…