Related papers: Koll\'ar's injectivity theorem for globally $F$-re…

A vector variational principle is proved.

We give an effective infinitesimal Torelli theorem for cyclic covers of G/P, where G is a simple algebraic group and P is a maximal parabolic subgroup.

We prove a general form of Green Formula and Cauchy Integral Theorem for arbitrary closed rectifiable curves in the plane.

Inspired by the inductive proof of LYM-inequality given by P. Frankl, we provide an inductive proof of the Bollob\'{a}s two family theorem.

We prove the theorem converse to Jackson's theorem for a modulus of smoothness of the first order generalised by means of an asymmetric operator of generalised translation.

A combinatorial proof of the unimodality of the generalized q-Gaussian coefficients based on the explicit formula for Kostka-Foulkes polynomials is given.

Various characterizations are offered of injectivity of the canonical fundamental group homomorphism for a certain class of inverse limit spaces. One application characterizes the existence of a kind of generalized universal cover.

Combining P\'{o}sa's rotation lemma with a technique of Kopylov in a novel approach, we prove a generalization of the Erd\H{o}s-Gallai theorems on cycles and paths. This implies a clique version of the Erd\H{o}s-Gallai stability theorems…

Suppose that $(\mathcal{F},\mathcal{M})$ is an injective structure of $R$-Mod such that the class $\mathcal{F}$ is closed for direct limits, then two modules in $\mathcal{M}$ are isomorphic if there are maps in $\mathcal{F}$ from each one…

We prove a structure theorem for the Gromov-Witten invariants of compact Kahler surfaces with geometric genus $p_g>0$. Under the technical assumption that there is a canonical divisor that is a disjoint union of smooth components, the…

We present a general theorem which computes the cohomology of a homological vector field on global sections of vector bundles over smooth affine supervarieties. The hypotheses and results have the clear flavor of a localization theorem.

Using a mixed-characteristic incarnation of fusion, we prove an analog of Nekov\'a\v{r}-Scholl's plectic conjecture for local Shimura varieties. We apply this to obtain results on the plectic conjecture for (global) Shimura varieties after…

We prove a companion forms theorem for mod l Hilbert modular forms. This work generalises results of Gross and Coleman--Voloch for modular forms over Q, and gives a new proof of their results in many cases. The methods used are completely…

The theorem of Mather on generic projections of smooth algebraic varieties is also proved for the singular ones.

We prove the finiteness of the kernel of the localization map in the Galois cohomology of a connected reductive group over a global field

We propose two inductive approaches for determining the cohomology of Deligne-Lusztig varieties in the case of the general linear group

The K-theory of a functor may be viewed as a relative version of the K-theory of a ring. In the case of a Galois extension of a number field F/L with rings of integers A/B respectively, this K-theory of the "norm functor" is an extension of…

We prove a generalization of Fulton's conjecture which relates intersection theory on an arbitrary flag variety to invariant theory.

We construct an Euler system -- a compatible family of global cohomology classes -- for the Galois representations appearing in the geometry of Hilbert modular surfaces. If a conjecture of Bloch and Kato on injectivity of regulator maps…

Kolmogorov's invariant torus theorem is proved using a simple fixed point theorem.