Further Counterexamples to Zarhin's conjecture about micro weights

TL;DR

This paper introduces new counterexamples to Zarhin's conjecture on micro weights in positive characteristic, detailing their dimensions and Newton slopes, thus challenging existing beliefs in algebraic geometry.

Contribution

It provides two new families of Abelian varieties that contradict Zarhin's conjecture, with explicit calculations of their dimensions and Newton slopes.

Findings

Discovered two new counterexamples to Zarhin's conjecture.

Determined the dimension and Newton slopes of the ghost Abelian varieties.

Challenged the validity of Zarhin's conjecture in positive characteristic.

Abstract

We present two new families of Abelian varieties which contradict Zarhin's conjecture about micro weights in positive characteristics. For each of these examples we determine the dimension and the Newton slopes of the ghost Abelian variety in the sense of Cadoret and Tamagawa.