Iwasawa theory of Frobenius-torsion class group schemes

TL;DR

This paper develops a new Iwasawa theory for Frobenius kernels on Jacobians in characteristic p, confirming several main conjectures related to geometric Z_p-towers over the projective line.

Contribution

It introduces a novel Iwasawa theoretical framework for Frobenius-torsion class group schemes in characteristic p, proving key conjectures in the field.

Findings

Established a new Iwasawa theory for Frobenius kernels on Jacobians.

Proved several main conjectures from prior work.

Enhanced understanding of class group schemes in characteristic p.

Abstract

We establish a new Iwasawa theory for the kernel of Frobenius on Jacobians of curves in geometric $\mathbf{Z}_p$-towers over the projective line in characteristic $p$, thereby proving several of the main conjectures of [arXiv:2107.12555].