Frobenius transformation, mirror map and instanton numbers
Albert Schwarz, Vadim Vologodsky
TL;DR
This paper links Frobenius transformations on p-adic cohomology of Calabi-Yau threefolds with mirror maps and instanton numbers, providing a p-adic perspective on Gopakumar-Vafa invariants.
Contribution
It expresses Frobenius transformations in terms of mirror maps and instanton numbers, offering a new p-adic interpretation of Gopakumar-Vafa invariants' integrality.
Findings
Frobenius transformation can be expressed via mirror map and instanton numbers.
Mirror map is described through Frobenius transformation on p-adic cohomology.
Provides a p-adic interpretation of Gopakumar-Vafa invariants' integrality.
Abstract
We show that one can express Frobenius transformation on middle-dimensional p-adic cohomology of Calabi-Yau threefold in terms of mirror map and instanton numbers. We express the mirror map in terms of Frobenius transformation on p-adic cohomology . We discuss a -adic interpretation of the conjecture about integrality of Gopakumar-Vafa invariants.
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