Supersingularity of Motives with Complex Multiplication and a Twisted Polarization

TL;DR

This paper establishes a unified criterion for supersingularity in varieties with large automorphism groups and perfect pairings, extending known results and applying notably to Artin-Schreier curves.

Contribution

It introduces a new criterion for supersingularity that generalizes previous results and applies to a broad class of curves with complex multiplication.

Findings

Unified supersingularity criterion for varieties with automorphisms

Extension of known results to new classes of curves

Application to Artin-Schreier curves

Abstract

In this note, we prove a criteria for supersingularity when the variety has a large automorphism group and a perfect bilinear pairing. This criteria unifies and extends many known results on the supersingularity of curves and varieties and in particular, applies to a large family of Artin-Schreier curves.