Canonical Lifts of Cycle Classes of Sections

TL;DR

This paper constructs canonical lifts of cycle classes associated with sections of p-adic curves to their models' cohomology, addressing a key question in anabelian geometry.

Contribution

It provides a new method for lifting cycle classes canonically to the cohomology of proper models, advancing understanding in p-adic anabelian geometry.

Findings

Constructed canonical lifts of cycle classes for p-adic curves.

Answered a question posed by Esnault and Wittenberg.

Enhances tools for studying sections of p-adic curves.

Abstract

We present the construction of canonical lifts of $\ell$-adic cycle classes of sections of $p$-adic projective anabelian curves to the cohomology of arbitrary proper, regular, flat models. This answers a question of Esnault and Wittenberg.