Related papers: Finite polynomial cohomology for general varieties

We compute syntomic cohomology of semistable affinoids in terms of cohomology of $(\varphi,\Gamma)$-modules which, thanks to work of Fontaine-Herr, Andreatta-Iovita, and Kedlaya-Liu, is known to compute Galois cohomology of these affinoids.…

We give the geometric version of a construction of Colmez-Niziol which establishes a comparison theorem between arithmetic p-adic nearby cycles and syntomic sheaves. The local construction of the period isomorphism uses…

This paper is devoted to the horizontal (``characteristic'') cohomology of systems of differential equations. Recent results on computing the horizontal cohomology via the compatibility complex are generalized. New results on the Vinogradov…

In this short note, we prove a result about the non-generic part of the cohomology of certain compact unitary Shimura varieties for good $p$, partially extending a result of Boyer in the case of Harris--Taylor unitary Shimura varieties. Our…

In the present review we provide an extensive analysis of the intertwinement between Feynman integrals and cohomology theories in the light of the recent developments. Feynman integrals enter in several perturbative methods for solving non…

For any type of fundamental groupoid scheme, we construct an algebraic cohomology theory for varieties with coefficients in the base field. This is a minor variant of \'etale cohomology, involving neither de Rham complexes nor…

This article investigates equivariant parametrized cellular cohomology, a cohomology theory introduced by Costenoble-Waner for spaces with an action by a compact Lie group $G$. The theory extends the $RO(G)$-graded cohomology of a $G$-space…

The goal of this paper is to offer a new construction of the de Rham-Witt complex of smooth varieties over perfect fields of characteristic $p>0$. We introduce a category of cochain complexes equipped with an endomorphism $F$ of underlying…

In local relative $p$-adic Hodge theory, we show that the Galois cohomology of a finite height crystalline representation (up to a twist) is essentially computed via the (Fontaine--Messing) syntomic complex with coefficients in the…

We give a short new computation of the quantum cohomology of an arbitrary smooth toric variety $X$, by showing directly that the Kodaira-Spencer map of Fukaya-Oh-Ohta-Ono defines an isomorphism onto a suitable Jacobian ring. The proof is…

We generalize the strong comparison theorem of Franjou, Friedlander, Scorichenko and Suslin to the setting of Fp-linear additive categories. Our results have a strong impact in terms of explicit computations of functor homology, and they…

We begin by introducing schemes of binoids, invertible $\mathcal{O}_M$-sets and cohomology of sheaves of abelian groups defined on schemes of binoids. We define the so-called punctured combinatorial \v{C}ech-Picard complex, whose first…

We construct a K-theory version of Bhatt-Morrow-Scholze's Breuil-Kisin cohomology theory for $\sO_K$-linear idempotent-complete, small smooth proper stable infinity-categories, where $K$ is a discretely valued extension of $\Q_p$ with…

Thin homotopies, introduced by Caetano-Picken, serve to axiomatize the holonomy of connections on principal bundles. This approach has been generalized to higher non-abelian bundles with connection through transport functors and higher…

This article gives an expository account of quasisyntomic descent and the Nygaard filtration in positive characteristic, complemented by several new applications to $p$-adic cohomology theories. The guiding result is a new approach to…

We show that if an inclusion of finite groups H < G of index prime to p induces a homeomorphism of mod p cohomology varieties, or equivalently an F-isomorphism in mod p cohomology, then H controls p-fusion in G, if p is odd. This…

We propose a natural extension of the Novikov numbers for the basic cohomology class of a closed basic $1$-form on a proper Lie groupoid of finitely generated type. As an application, we prove corresponding Novikov inequalities for compact…

We generalize the functorial quasi-isomorphism in \cite{Davis2011} from overconvergent Witt de-Rham cohomology to rigid cohomology on smooth varieties over a finite field $k$, dropping the quasi-projectiveness condition. We do so by…

In this paper we suggest a new general formalism for studying the invariants of polyhedra and manifolds comming from the theory of von Neumann algebras. First, we examine generality in which one may apply the construction of the extended…

In the context of orientable circuits and subcomplexes of these as representing certain singular spaces, we consider characteristic class formulas generalizing those classical results as seen for the Riemann-Hurwitz formula for regulating…