Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userChow-Witt rings of Grassmannians
74
0
0.0
(
0
)
Authors
Matthias Wendt
Ask ChatGPT about the research
No Arabic abstract
We complement our previous computation of the Chow-Witt rings of classifying spaces of special linear groups by an analogous computation for the general linear groups. This case involves discussion of non-trivial dualities. The computation proceeds along the lines of the classical computation of the integral cohomology of ${rm BO}(n)$ with local coefficients, as done by Cadek. The computations of Chow-Witt rings of classifying spaces of ${rm GL}_n$ are then used to compute the Chow-Witt rings of the finite Grassmannians. As before, the formulas are close parallels of the formulas describing integral cohomology rings of real Grassmannians.
rate research
Read More
Let the vector bundle $mathcal{E}$ be a deformation of the tangent bundle over the Grassmannian $G(k,n)$. We compute the ring structure of sheaf cohomology valued in exterior powers of $mathcal{E}$, also known as the polymology. This is the first part of a project studying the quantum sheaf cohomology of Grassmannians with deformations of the tangent bundle, a generalization of ordinary quantum cohomology rings of Grassmannians. A companion physics paper [arXiv:1512.08586] describes physical aspects of the theory, including a conjecture for the quantum sheaf cohomology ring, and numerous examples.
In these lectures, we provide a toolkit to work with Chow-Witt groups, and more generally with the homology and cohomology of the Rost-Schmid complex associated to Milnor-Witt $K$-theory.
In this paper, we construct a $q$-deformation of the Witt-Burnside ring of a profinite group over a commutative ring, where $q$ ranges over the set of integers. When $q=1$, it coincides with the Witt-Burnside ring introduced by A. Dress and C. Siebeneicher (Adv. Math. {70} (1988), 87-132). To achieve our goal we first show that there exists a $q$-deformation of the necklace ring of a profinite group over a commutative ring. As in the classical case, i.e., the case $q=1$, q-deformed Witt-Burnside rings and necklace rings always come equipped with inductions and restrictions. We also study their properties. As a byproduct, we prove a conjecture due to Lenart (J. Algebra. 199 (1998), 703-732). Finally, we classify $mathbb W_G^q$ up to strict natural isomorphism in case where $G$ is an abelian profinite group.
Let $X$ be an integral scheme of finite presentation over a field. Let $q$ be a singular closed point of $X$. We prove that there exists an open subset $V$ of $X$ containing $q$ such that $V$ admits a resolution, that is, there exists a smooth scheme $widetilde V$ and a proper birational morphism from $widetilde V$ onto $V$.
We introduce a theory of multigraded Cayley-Chow forms associated to subvarieties of products of projective spaces. Two new phenomena arise: first, the construction turns out to require certain inequalities on the dimensions of projections; and second, in positive characteristic the multigraded Cayley-Chow forms can have higher multiplicities. The theory also provides a natural framework for understanding multifocal tensors in computer vision.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
