Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2404.06697

Bredon motivic cohomology of the real numbers

Bill Deng·Mircea Voineagu
View original source ↗Read source document ↗Export metadata ↓

Abstract

Over the real numbers with $\Z/2-$coefficients, we compute the $C_2$-equivariant Borel motivic cohomology ring, the Bredon motivic cohomology groups and prove that the Bredon motivic cohomology ring of the real numbers is a proper subring in the $RO(C_2\times C_2)$-graded Bredon cohomology ring of a point. This generalizes Voevodsky's computation of the motivic cohomology ring of the real numbers to the $C_2$-equivariant setting. These computations are extended afterwards to any real closed field.

Explore related subjects

math.AGmath.ATmath.KT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Bill Deng, Mircea Voineagu. 2025-05-26. Bredon motivic cohomology of the real numbers. https://arxiv.org/abs/2404.06697

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

G3-Criteria and Applications

The G3-property of a subvariety was introduced by Hironaka-Matsumura, and plays an important role for deducing connectedness and extension results. Unfortunately, it's a rather elusive notion, which is not always easy to establish. Most of the existing work is concentrated on subvarieties of homogeneous varieties. The first goal of this article is to show that mobility assumptions on the subvariety, considered in works of Badescu, Chow, Debarre, Voisin, yield a certain partial positivity property, slightly stronger than G3, previously introduced by the author. Second, we apply the result to prove that, in numerous situations, the splitting of the normal bundle of a smooth two-codimensional subvariety implies that it is a complete intersection.

math.AG↗
arXiv2026

Nodal degeneration of chiral algebras I: Global structure and gluing formula

We define a natural extension of a universal factorization algebra $\mathcal{A}$ to families of stable punctured curves, by integrating over all semistable modifications. We prove that the resulting sheaf of factorization homology satisfies a natural gluing formula, by tensoring over a certain derived associative algebra $\mathfrak{Z}_{\mathcal{A}}^0$, generalizing the Verlinde formula for gluing of conformal blocks.

math.AG↗