相关论文: Prismatic cohomology and de Rham-Witt forms

We compute the coherent cohomology of the structure sheaf of complex periplectic Grassmannians. In particular, we show that it can be decomposed as a tensor product of the singular cohomology ring of a Grassmannian for either the symplectic…

By a theorem of Bernhard Keller the de Rham cohomology of a smooth variety is isomorphic to the periodic cyclic homology of the differential graded category of perfect complexes on the variety. Both the de Rham cohomology and the cyclic…

By studying cohomology classes that are related with $p$-harmonic morphisms, $F$-harmonic maps, and $f$-harmonic maps, we extend several of our previous results on Riemannian submersions and $p$-harmonic morphisms to $F$-harmonic maps, and…

We make explicit some conditions on a semi-abelian category D such that, for any abelian group A in D and any object Y in D, the cohomology group homomorphisms with coefficients in A, induced by the inclusion of the abelian objects of D at…

Two continuous maps $f, g : \mathbb{C}^2\to\mathbb{C}^2$ are said to be topologically equivalent if there exist homeomorphisms $\varphi,\psi:\mathbb{C}^2\to\mathbb{C}^2$ satisfying $\psi\circ f\circ\varphi = g$. It is known that there are…

We construct a natural filtration on $T(1)$-local $\mathrm{TC}$ for any animated commutative rings using prismatic cohomology and descent theory. In the course of the construction, we also study some general properties of prismatic…

We define the motivic filtrations on real topological Hochschild homology and its companions. In particular, we prove that real topological cyclic homology admits a natural complete filtration whose graded pieces are equivariant suspensions…

An algebra $A$ with identity $(a\circ b)\circ c-a\circ(b\circ c)=(a\circ c)\circ b-a\circ(c\circ b),$ is called right-symmetric. Cohomology and deformation theory for right-symmetric algebras are developed. Cohomologies of $gl_n$ and…

In this paper, we study the cohomology of semisimple local systems in the spirit of classical Hodge theory. On the one hand, we establish a generalization of Hodge-Riemann bilinear relations. For a semisimple local system on a smooth…

We construct the crystalline comparison isomorphisms for proper smooth formal schemes over an absolutely unramified base. Such isomorphisms hold for \'etale cohomology with nontrivial coefficients, as well as in the relative setting, i.e.…

Let R be a perfect F_p-algebra, equipped with the trivial norm. Let W(R) be the ring of p-typical Witt vectors over R, equipped with the p-adic norm. At the level of nonarchimedean analytic spaces (in the sense of Berkovich), we demonstrate…

We explicitly describe cohomology of the sheaf of differential forms with poles along a semiample divisor on a complete simplicial toric variety. As an application, we obtain a new vanishing theorem which is an analogue of the…

We show that the natural map from the syntomification of a ring $R$ to the stack of $R$-algebra stacks is fully faithful, answering a question of Drinfeld, and we describe its essential image in terms of underlying monoid stacks. We also…

We establish basic facts about the varieties of homogeneous polynomials divisible by powers of linear forms, and explain consequences for geometric complexity theory. This includes quadratic set-theoretic equations, a description of the…

A cosmological polytope is defined for a given Feynman diagram, and its canonical form may be used to compute the contribution of the Feynman diagram to the wavefunction of certain cosmological models. Given a subdivision of a polytope, its…

It is well known that the validity of the so called Lenard-Magri scheme of integrability of a bi-Hamiltonian PDE can be established if one has some precise information on the corresponding 1st variational Poisson cohomology for one of the…

We compute the canonical form of the cosmological polytope for any graph in terms of the dual of the shifted cosmological polytope in two different ways. On the way, we provide an explicit coordinate description of the dual of the…

This paper provides a rigorous account on the geometry of forms on supermanifolds, with a focus on its algebraic-geometric aspects. First, we introduce the de Rham complex of differential forms and we compute its cohomology. We then discuss…

We establish the formula for multiplication by the class of a special Schubert variety in the integral cohomology ring of the flag manifold. This formula also describes the multiplication of a Schubert polynomial by either an elementary…

Over a perfect field $k$ of characteristic $p > 0$, we construct a ``Witt vector cohomology with compact supports'' for separated $k$-schemes of finite type, extending (after tensorisation with $\mathbb{Q}$) the classical theory for proper…