Motivic Gauss and Jacobi sums
Abstract
We study the Gauss and Jacobi sums from a viewpoint of motives. We exhibit isomorphisms between Chow motives arising from the Artin–Schreier curve and the Fermat varieties over a finite field, that can be regarded as (and yield a new proof of) classically known relations among Gauss and Jacobi sums such as Davenport–Hasse’s multiplication formula. As a key step, we define motivic analogues of the Gauss and Jacobi sums as algebraic correspondences, and show that they represent the Frobenius endomorphisms of such motives. This generalizes Coleman’s result for curves. These results are applied to investigate the group of invertible Chow motives with coefficients in a cyclotomic field.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Analytic Number Theory Research
Publication details
- Journal / source
- Annales de la faculté des sciences de Toulouse Mathématiques
- Volume
- 35
- Issue
- 1
- Pages
- 95–135
- Publication date
- 13 January 2026
- Language
- EN