Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAn algorithm for de Rham cohomology groups of the complement of an affine variety via D-module computation
66
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We give an algorithm to compute the following cohomology groups on $U = C^n setminus V(f)$ for any non-zero polynomial $f in Q[x_1, ..., x_n]$; 1. $H^k(U, C_U)$, $C_U$ is the constant sheaf on $U$ with stalk $C$. 2. $H^k(U, Vsc)$, $Vsc$ is a locally constant sheaf of rank 1 on $U$. We also give partial results on computation of cohomology groups on $U$ for a locally constant sheaf of general rank and on computation of $H^k(C^n setminus Z, C)$ where $Z$ is a general algebraic set. Our algorithm is based on computations of Grobner bases in the ring of differential operators with polynomial coefficients.
rate research
Read More
We use the Beilinson $t$-structure on filtered complexes and the Hochschild-Kostant-Rosenberg theorem to construct filtrations on the negative cyclic and periodic cyclic homologies of a scheme $X$ with graded pieces given by the Hodge-completion of the derived de Rham cohomology of $X$. Such filtrations have previously been constructed by Loday in characteristic zero and by Bhatt-Morrow-Scholze for $p$-complete negative cyclic and periodic cyclic homology in the quasisyntomic case.
The title refers to the nilcommutative or $NC$-schemes introduced by M. Kapranov in math.AG/9802041. The latter are noncommutative nilpotent thickenings of commutative schemes. We consider also the parallel theory of nil-Poisson or $NP$-schemes, which are nilpotent thickenings of commutative schemes in the category of Poisson schemes. We study several variants of de Rham cohomology for $NC$- and $NP$-schemes. The variants include nilcommutative and nil-Poiss
We provide a new formalism of de Rham--Witt complexes in the logarithmic setting. This construction generalizes a result of Bhatt--Lurie--Mathew, and agrees with those of Hyodo--Kato and Matsuue for log-smooth schemes of log-Cartier type. We then apply our formalism to obtain a more direct proof of the log crystalline comparison of A_inf-cohomology in the case of semistable reduction, which is established by Cesnavicius--Koshiwara.
For a natural number $m$, let $mathcal{S}_m/mathbb{F}_2$ be the $m$th Suzuki curve. We study the mod $2$ Dieudonn{e} module of $mathcal{S}_m$, which gives the equivalent information as the Ekedahl-Oort type or the structure of the $2$-torsion group scheme of its Jacobian. We accomplish this by studying the de Rham cohomology of $mathcal{S}_m$. For all $m$, we determine the structure of the de Rham cohomology as a $2$-modular representation of the $m$th Suzuki group and the structure of a submodule of the mod $2$ Dieudonn{e} module. For $m=1$ and $2$, we determine the complete structure of the mod $2$ Dieudonn{e} module.
We present a study on the integral forms and their Cech/de Rham cohomology. We analyze the problem from a general perspective of sheaf theory and we explore examples in superprojective manifolds. Integral forms are fundamental in the theory of integration in supermanifolds. One can define the integral forms introducing a new sheaf containing, among other objects, the new basic forms delta(dtheta) where the symbol delta has the usual formal properties of Diracs delta distribution and acts on functions and forms as a Dirac measure. They satisfy in addition some new relations on the sheaf. It turns out that the enlarged sheaf of integral and ordinary superforms contains also forms of negative degree and, moreover, due to the additional relations introduced, its cohomology is, in a non trivial way, different from the usual superform cohomology.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
