Grothendieck’s period conjecture for Kummer surfaces of self-product CM type
Abstract
We show that the Grothendieck period conjecture holds for the Kummer surface associated with the square of a complex muliplication (CM) elliptic curve. This means that the period isomorphism is dense in the torsor of motivic periods. In other words, the isomorphism is dense in the torsor of motivated periods, and motivated classes on powers of the surface are algebraic. The point is that the motive has a nontrivial transcendental part but belongs to the Tannakian category generated by the motive of a CM elliptic curve.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Geometric and Algebraic Topology
Publication details
- Journal / source
- Kyoto journal of mathematics
- Publisher
- Duke University Press
- Volume
- 66
- Issue
- 3
- Pages
- 601-612
- Publication date
- 8 May 2026
- Language
- EN