Related papers: A remark on Ehresmann's Fibration Theorem

We give an elementary short proof of Grothendieck's base change theorem for the cohomology of flat coherent sheaves.

In his 2011 paper, Teleman proved that a cohomological field theory on the moduli space $\overline{\mathcal{M}}_{g,n}$ of stable complex curves is uniquely determined by its restriction to the smooth part $\mathcal{M}_{g,n}$, provided that…

We describe some of the connections between the Bieri-Neumann-Strebel-Renz invariants, the Dwyer-Fried invariants, and the cohomology support loci of a space X. Under suitable hypotheses, the geometric and homological finiteness properties…

We present a development of cellular cohomology in homotopy type theory. Cohomology associates to each space a sequence of abelian groups capturing part of its structure, and has the advantage over homotopy groups in that these abelian…

We prove a connexity theorem for abelian varieties in characteristic $0$: if $X$ is an abelian variety and $V\rightarrow X$ and $W\rightarrow X$ two morphisms, then, under certain hypotheses, the fiber product of $V$ and $W$ over $X$ is…

We study the conservativity of extensions by additional strict equalities of dependent type theories (and more general second-order generalized algebraic theories). The conservativity of Extensional Type Theory over Intensional Type Theory…

In this paper, we develop $L^2$ theory for Riemannian and Hermitian foliations on manifolds with basic boundary. We establish a decomposition theorem, various vanishing theorems, a twisted duality theorem for basic cohomologies and an…

Given a smooth foliation on a closed manifold, basic forms are differential forms that can be expressed locally in terms of the transverse variables. The space of basic forms yields a differential complex, because the exterior derivative…

For a natural class of cohomology theories with support (including \'etale or pro-\'etale cohomology with suitable coefficients), we prove a moving lemma for cohomology classes with support on smooth quasi-projective k-varieties that admit…

We explore the relationship between fibrations arising naturally from a surjective morphism to an abelian variety. These fibrations encode geometric information about the morphism. Our study focuses on the interplay of these fibrations and…

This paper is a continuation of a previous paper joint with Dennis Sullivan (arXiv:1704.04308). Working in the context of commutative differential graded algebras, we study the ideal of the cohomology classes which can be annihilated by…

We prove that under restrictions on the fiber, any fibered partially hyperbolic system over a nilmanifold is leaf conjugate to a smooth model that is isometric on the fibers and descends to a hyperbolic nilmanifold automorphism on the base.…

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.

The idea of the work is to find an invariant way to pass from deformation theory to cohomology, which does not use any explicit cocycles. The appropriate cohomology theory is based on considering sheaves on a certain site. An advantage of…

We give a simple proof for the rigidity of a complex in the bounded derived category of sheaves with constructible cohomology on an abelian variety.

Motivated by an example, due to Voisin, of a smooth simply-connected projective variety with trivial canonical class and cyclic Picard group, admitting a meromorphic endomorphism of high degree, we study meromorphic fibrations on certain…

In this article we study cohomology of a group with coefficients in representations on Banach spaces and its stability under deformations. We show that small, metric deformations of the representation preserve vanishing of cohomology. As…

In this article, we introduce some generalized Hardy spaces on fibrations of planar domains and fibrations of products of planar domains. We consider the kernel functions on these spaces, and we prove some weighted versions of Saitoh's…

Birkhoff's variety theorem, a fundamental theorem of universal algebra, asserts that a subclass of a given algebra is definable by equations if and only if it satisfies specific closure properties. In a generalized version of this theorem,…

The nth symmetric product of a Riemann surface carries a natural family of Kaehler forms, arising from its interpretation as a moduli space of abelian vortices. We give a new proof of a formula of Manton-Nasir for the cohomology classes of…