On the image of higher signature maps
Abstract
Given a smooth variety $X$ over the field $\mathbb{R}$ of real numbers and a line bundle $\mathcal{L}$ on $X$ with associated topological line bundle $L=\mathcal{L}(\mathbb{R})$, we study the quadratic real cycle class map $\widetildeγ_{\mathbb{R}}^c:\widetilde{\mathrm{CH}}^c(X,\mathcal{L})\rightarrow\mathrm{H}^c(X(\mathbb{R}),\mathbb{Z}(L))$ from the $c$-th Chow-Witt group of $X$ to the $c$-th cohomology group of its real locus $X(\mathbb{R})$ with coefficients in the local system $\mathbb{Z}(L)$ associated with $L$. We focus on the cases $c\in\{0,d-2,d-1,d\}$ where $d$ is the dimension of $X$ and we formulate a precise conjecture on the image of $\widetildeγ_{\mathbb{R}}$ in terms of the exponents of its cokernel that is corroborated by the results obtained in those codimensions.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Analytic Number Theory Research
Mathematics and Applications
Publication details
- Journal / source
- Annals of K-Theory
- Publisher
- Mathematical Sciences Publishers
- Volume
- 11
- Issue
- 2
- Pages
- 171–212
- Publication date
- 30 March 2026
- Language
- EN