Divisibility of characteristic numbers

TL;DR

This paper employs homotopy theory to define rational characteristic numbers with integral values, establishing a degree formula that links divisibility properties to morphisms between algebraic varieties.

Contribution

It introduces a novel homotopy-theoretic approach to characteristic numbers, providing new degree formulas and divisibility criteria relevant to algebraic geometry.

Findings

Established a nontrivial degree formula for characteristic numbers.

Linked divisibility properties of characteristic numbers to morphisms between varieties.

Provided criteria for the existence of zero cycles based on divisibility.

Abstract

We use homotopy theory to define certain rational coefficients characteristic numbers with integral values, depending on a given prime number q and positive integer t. We prove the first nontrivial degree formula and use it to show that existence of morphisms between algebraic varieties for which these numbers are not divisible by q give information on the degree of such morphisms or on zero cycles of the target variety.