Frobenius map for quintic threefolds
I. Shapiro
TL;DR
This paper computes the Frobenius map matrix on the middle cohomology of a family of quintic threefolds, revealing insights into their arithmetic properties via mirror symmetry.
Contribution
It provides an explicit calculation of the Frobenius map matrix for a family of quintic threefolds, connecting mirror symmetry with arithmetic geometry.
Findings
Explicit Frobenius matrix for the family of quintic threefolds
Insights into the arithmetic structure of these threefolds
Connections established between mirror symmetry and Frobenius action
Abstract
We calculate the matrix of the Frobenius map on the middle dimensional cohomology of the one parameter family that is related by mirror symmetry to the family of all quintic threefolds.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry