Uniform bounds for obstructions to the integral Tate conjecture

TL;DR

This paper establishes uniform bounds on obstructions to the integral Tate conjecture within 1-dimensional families of algebraic varieties, assuming certain variational realization conjectures, advancing understanding of algebraic cycles.

Contribution

It provides the first uniform bounds for obstructions to the integral Tate conjecture under specific conjectural assumptions.

Findings

Uniform bounds are derived for obstructions in algebraic families.

Results depend on variational realization conjectures.

Advances the theoretical framework for the integral Tate conjecture.

Abstract

Assuming natural variational realization conjectures, we give uniform bounds for the obstruction to the integral Tate conjecture in 1-dimensional families of algebraic varieties over an infinite finitely generated field.