Related papers: Universal Weil cohomology

An extension to higher dimensions of the Bel-Debever characterization of the Weyl tensor is considered. This provides algebraic conditions that uniquely determine the multiplicity of a Weyl aligned null direction (WAND), and thus the…

We extend Tate duality for Galois cohomology of abelian varieties to $1$-motives over a $p$-adic field, improving a result of Harari and Szamuely. To do this, we replace Galois cohomology with the condensed cohomology of the Weil group.…

We introduce a systematic theory of Weil bundles over \( p \)-adic analytic manifolds, forging new connections between differential calculus over non-archimedean fields and arithmetic geometry. By developing a framework for infinitesimal…

We prove a K\"unneth-type equivalence of derived categories of lisse and constructible Weil sheaves on schemes in characteristic $p > 0$ for various coefficients, including finite discrete rings, algebraic field extensions $E \supset…

We prove a universal coefficients theorem for the overconvergent cohomology modules introduced by Ash and Stevens, and give several applications. In particular, we sketch a very simple construction of eigenvarieties using overconvergent…

We study the multiplicities of pure motives modulo numerical equivalence, which are defined as scalars comparing the tannakian trace with the ring-theoretic trace. Our general set-up is that of a rigid semi-simple tensor category such that…

Let M be a Poisson manifold and A a Weil algebra. We describe an isomorphism of cohomolgy algebra and proves that Poisson cohomology with values in A is isomorphic to the tensor product of A with Poisson cohomolgy with real values.

This article contains a new argument which proves vanishing of the first cohomology for negative vector bundles over a complex projective variety if the rank of the bundle is smaller than the dimension of the base. Similar argument is…

We develop the global moduli theory of symplectic varieties in the sense of Beauville. We prove a number of analogs of classical results from the smooth case, including a global Torelli theorem. In particular, this yields a new proof of…

Motivated by Murre's work on universal regular homomorphisms on Chow groups in codimension $2,$ we generalize the algebraic equivalence relation and regular homomorphisms to the context of Voevodsky motives over a field. In the Nisnevich…

Recent developments in motivic homotopy theory, especially the construction of norm functors by Bachmann and Hoyois, rely heavily on the machinery of infinite categories. In this paper, we take a purely geometric and elementary approach via…

Let k be an algebraically closed field of characteristic p>0. Let W(k) be the ring of Witt vectors with coefficients in k. We prove a motivic conjecture of Milne that relates, in the case of abelian schemes, the \'etale cohomology with…

It is known that the etale cohomology of a potentially good abelian variety over a local field K is determined by its Euler factors over the extensions of K. We extend this to all abelian varieties, show that it is enough to take extensions…

Assuming the K\"unneth type standard conjecture, we propose a way to describe objects of mixed motives explicitly. We study their formal properties, and we associate mixed motives to schemes smooth and separated over a field. This serves as…

The deepest arithmetic invariants attached to an algebraic variety defined over a number field $F$ are conjecturally captured by the integral part of its motivic cohomology. There are essentially two ways of defining it when $X$ is a smooth…

Let k be a base field of positive characteristic. Making use of topological periodic cyclic homology, we start by proving that the category of noncommutative numerical motives over k is abelian semi-simple, as conjectured by Kontsevich.…

In this article we study the cohomological and homological (due to Jannsen) Hodge conjecture for singular varieties. The motivation for studying singular varieties comes from the fact that any smooth projective variety X is birational to a…

We explain how Teleman quantization can be applied to moduli spaces of quiver representations to compute the higher cohomology of the endomorphism bundle of the universal bundle. We use this to prove Schofield's partial tilting conjecture,…

We present a new coherence theorem for comprehension categories, providing strict models of dependent type theory with all standard constructors, including dependent products, dependent sums, identity types, and other inductive types.…

We introduce global model categories as a general framework to capture several phenomena in global equivariant homotopy theory. We then construct genuine stabilizations of these, generalizing the usual passage from unstable to stable global…