相关论文: Vanishing of cohomology associated to quantized Dr…

We study the Ramond twisted representations of the affine W-algebra W^k(g,f) in the case that f admits a good even grading. We establish the vanishing and the almost irreducibility of the corresponding BRST cohomology. This confirms some of…

Using the work of Dwyer, Weiss, and Williams we associate an invariant to any topologically trivial family of smooth h-cobordisms. This invariant is called the smooth structure class, and is closely related to the higher Franz--Reidemeister…

Recently, by studying an explicit basis, K\"ock and Laurent give the decomposition of the $\overline{\mathbb{F}}_q[\mathrm{SL}_2(\mathbb{F}_q)]$-module of holomorphic forms on the Drinfeld curve. We present a crystalline cohomological proof…

For all algebraic groups over non-Archimedean local fields, the bounded cohomology vanishes. This follows from the corresponding statement for automorphism groups of Bruhat--Tits buildings, which hinges on the solution to the flatmate…

In 1989, D. Happel pointed out for a possible connection between the global dimension of a finite-dimensional algebra and its Hochschild cohomology: is it true that the vanishing of Hochschild cohomology higher groups is sufficient to…

We use the toric degeneration of Bott-Samelson varieties and the description of cohomolgy of line bundles on toric varieties to deduce vanishings results for the cohomology of lines bundles on Bott-Samelson varieties.

We prove a vanishing theorem for the cohomology of the complement of a complex hyperplane arrangement with coefficients in a complex local system. This result is compared with other vanishing theorems, and used to study Milnor fibers of…

We prove vanishing of cohomology with coefficients in representations on a large class of Banach spaces for a group acting "nicely" on a simplicial complexes based on spectral properties of the 1-dimensional links of the simplicial complex.

We formulate a series of conjectures on the stable tensor product of irreducible representations of symmetric groups, which are closely related to the reduced Kronecker coefficients. These conjectures are certain generalizations of…

We prove several asymptotic vanishing theorems for Frobenius twists of ample vector bundles in positive characteristic. As an application, we prove a generalization of the Bott-Danilov-Steenbrink vanishing theorem for ample vector bundles…

The q-deformed version of the Drinfeld-Sokolov reduction is extended to the case of the algebra of 'complex size matrices'; this construction generalizes earlier results of B.Khesin and F.Malikov on universal DS reduction and follows the…

For a large class of cohomology theories, we prove that refined unramified cohomology is canonically isomorphic to the hypercohomology of a natural truncated complex of Zariski sheaves. This generalizes a classical result of Bloch and Ogus…

The Feigin-Frenkel homomorphism underpinning the Wakimoto construction realises an affine Lie algebra at critical level in terms of the $\beta\gamma$-system of free fields. It was recently shown that much of the construction also goes…

We extend the techniques developed by Millson and Raghunathan to prove nonvanishing results for the cohomology of compact arithmetic quotients of hyperbolic n-space with values in the local coefficient systems associated to finite…

We initiate a study of cohomological aspects of weakly almost periodic group representations on Banach spaces, in particular, isometric representations on reflexive Banach spaces. Using the Ryll-Nardzewski fixed point Theorem, we prove a…

We reprove the theorem of Feigin and Frenkel relating the center of the critical level enveloping algebra of the Kac-Moody algebra for a semisimple Lie algebra to opers (which are certain de Rham local systems with extra structure) for the…

We give a proof of Artin's vanishing theorem in characteristic zero, based on Deligne's Riemann-Hilbert correspondence. Just as a curiosity.

Let (M,I,J,K) be a hyperkahler manifold of real dimension 4n, and L a non-trivial holomorphic line bundle on (M,I). Using the quaternionic Dolbeault complex, we prove the following vanishing theorem for holomorphic cohomology of L. If the…

This is an expository paper on Garland's vanishing theorem specialized to the case when the linear algebraic group is $\mathrm{SL}_n$. Garland's theorem can be stated as a vanishing of the cohomology groups of certain finite simplicial…

We prove the Second Vanishing Theorem for local cohomology modules of an unramified regular local ring in its full generality and provide a new proof of the Second Vanishing Theorem in prime characteristic $p$. As an application of our…