Related papers: Logarithmic Prismatic Cohomology I
We consider a finite group acting on a vector space and the corresponding skew group algebra generated by the group and the symmetric algebra of the space. This skew group algebra illuminates the resulting orbifold and serves as a…
We initiate a systematic study of cohomology theories for partial groups, algebraic structures introduced by Chermak that generalize groups by allowing only partially defined products. Inspired by classical group cohomology, we develop two…
We introduce the notion of a regular integrable connection on a smooth log scheme over $\mathbf{C}$ and construct an equivalence between the category of such connections and the category of integrable connections on its analytification,…
We define and study an integral refinement of the inverse of the Bloch-Kato exponential map which we call the de Rham logarithm. Our main tool to analyze the de Rham logarithm is the syntomic logarithm, a certain limit construction based on…
Let $X$ be an algebraic scheme over an algebraically closed field and $\ell$ a prime number invertible on $X$. According to classical results (due essentially to A. Grothendieck, M. Artin and P. Deligne), the \'etale cohomology groups…
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.…
Log prismatic cohomology theory developed by Koshikawa-Yao involves coefficient objects, called log prismatic $F$-crystals. In this paper, we construct and study realization functors from the category of log prismatic $F$-crystals to the…
The purpose of the present notes is to give a self-contained exposition on the use of the techniques of Nil-Hecke algebras in the localization approach to the equivariant Schubert calculus for cohomology of flag varieties. We also…
Let $\mathcal{A}$ be a connected cochain DG algebra such that its underlying graded algebra $\mathcal{A}^{\#}$ is the graded skew polynomial algebra $$k\langle x_1,x_2, x_3\rangle/\left(\begin{array}{ccc} x_1x_2+x_2x_1\\ x_2x_3+x_3x_2\\…
In this thesis we develop the cohomology of diagrams of algebras and then apply this to the cases of the $\lambda$-rings and the $\Psi$-rings. A diagram of algebras is a functor from a small category to some category of algebras. For an…
We relate the cohomology of the Orlik-Solomon algebra of a discriminantal arrangement to the local system cohomology of the complement. The Orlik-Solomon algebra of such an arrangement (viewed as a complex) is shown to be a linear…
Graded skew-commutative rings occur often in practice. Here are two examples: 1) The cohomology ring of a compact three-dimensional manifold. 2) The cohomology ring of the complement of a hyperplane arrangement (the Orlik-Solomon algebra).…
Staic defined symmetric cohomology of groups and studied that the secondary symmetric cohomology group is corresponding to group extensions and the injectivity of the canonical map from symmetric cohomology to classical cohomology. In this…
We construct a geometric version of BRST cohomology complex of a chiral module over a Lie-* algebra using the language of differential graded Lie algebroids in the category of D-modules on a compact curve $X$.
We introduce a variant of stable logarithmic maps, which we call punctured logarithmic maps. They allow an extension of logarithmic Gromov-Witten theory in which marked points have a negative order of tangency with boundary divisors. As a…
In this paper, we prove a $\partial\bar{\partial}$-type lemma on compact K\"ahler manifolds for logarithmic differential forms valued in the dual of a certain pseudo-effective line bundle, thereby confirming a conjecture proposed by X. Wan.…
Let X be Drinfeld's half space over a p-adic field K. The de Rham cohomology of X was first computed by Schneider and Stuhler. Afterwards there were given different proofs by Alon, de Shalit, Iovita and Spiess. This paper presents yet…
By a result of Gerstenhaber and Schack the simplicial cohomology ring $H^*(\mathcal{C};k)$ of a poset $\mathcal{C}$ is isomorphic to the Hochschild cohomology ring $HH^*(k\mathcal{C})$ of the category algebra $k\mathcal{C}$, where the poset…
Graded skew-commutative rings occur often in practice. Here are two examples: 1) The cohomology ring of a compact three-dimensional manifold. 2) The cohomology ring of the complement of a hyperplane arrangement (the Orlik-Solomon algebra).…
We study the quotient complex $\Delta (B_{lm})/S_l\wr S_m$ as a means of deducing facts about the ring $k[x_1,..., x_{lm}]^{S_l\wr S_m}$. It is shown in [He] that this quotient complex is shellable when $l=2$, implying Cohen-Macaulayness of…