Hasse-Witt invariants of Calabi-Yau varieties

TL;DR

This paper introduces two definitions of Hasse-Witt invariants for Calabi-Yau varieties, conjectures their equivalence, and supports this with numerous examples.

Contribution

It proposes a new dual approach to defining Hasse-Witt invariants and conjectures their equivalence, advancing understanding of Calabi-Yau varieties.

Findings

Two definitions of Hasse-Witt invariants are introduced.

Many examples support the conjecture of equivalence.

The paper links Cartier operator and Calabi-Yau modular forms.

Abstract

We define the Hasse-Witt invariant of Calabi-Yau varieties in two different ways. The first method is through Cartier operator and the second method is through the theory of Calabi-Yau modular forms developed by the third author. We conjecture that these two definitions are equivalent and provide many examples of Calabi-Yau varieties in support of this conjecture.