p-adic deformation of algebraic cycle classes

TL;DR

This paper investigates how algebraic cycle classes deform in p-adic settings, linking crystalline Chern characters and K-theory lifts to understand their p-adic deformation properties.

Contribution

It establishes a criterion connecting crystalline Chern characters and the lifting of vector bundle classes in K-theory for p-adic schemes.

Findings

Crystalline Chern character lies in a specific Hodge filtration part.

Vector bundle classes lift to pro-K-theory classes p-adically.

Deformation properties are characterized by these lifting conditions.

Abstract

We study the p-adic deformation properties of algebraic cycle classes modulo rational equivalence. We show that the crystalline Chern character of a vector bundle lies in a certain part of the Hodge filtration if and only if, rationally, the class of the vector bundle lifts to a formal pro-class in K-theory on the p-adic scheme.