Weak Arithmetic Cobordism

TL;DR

This paper extends Levine and Morel's algebraic cobordism to Arakelov varieties over number fields, integrating geometric and arithmetic aspects within Arakelov geometry.

Contribution

It refines the algebraic cobordism construction to an Arakelov setting, bridging geometric cobordism with arithmetic geometry over number fields.

Findings

Construction of an Arakelov version of algebraic cobordism.

Integration of cobordism theory into Arakelov geometry.

Potential applications to arithmetic invariants.

Abstract

In the early 2000's Levine and Morel have given a geometric construction of an algebraic cobordism group defined for all smooth quasi projective varieties over a field. We show how we can refine their construction to build an Arakelov version of this group for Arakelov varieties over a number field, and how this integrates well in the general philosophy of Arakelov geometry.