On rank $2$ hypergeometric motives

TL;DR

This paper investigates rank 2 hypergeometric motives, demonstrating their key properties and leveraging their rigidity to advance understanding of these special mathematical objects.

Contribution

The paper proves most expected properties of rank 2 hypergeometric motives, highlighting their rigidity and tractability compared to general motives.

Findings

Established key properties of rank 2 hypergeometric motives

Showed their rigidity simplifies analysis

Enhanced understanding of hypergeometric motives' structure

Abstract

Hypergeometric motives are family of motives associated to hypergeometric local systems. Their special features, in particular their rigidity, makes them more tractable than general motives. In the present article we prove most of the properties that they are expected to satisfy in the rank $2$ case.