Verdier hypercovering theorem for motivic spectra

TL;DR

This paper proves a Verdier Hypercovering Theorem for motivic spectra, enabling the construction of natural morphisms between different cohomology theories for complex varieties, extending existing maps.

Contribution

It introduces a Verdier Hypercovering Theorem for motivic spectra and constructs new morphisms between etale algebraic and Hodge filtered complex cobordism.

Findings

Established a Verdier Hypercovering Theorem for motivic spectra

Constructed a natural morphism from etale algebraic to Hodge filtered complex cobordism

Extended the map from etale motivic to Deligne-Beilinson cohomology

Abstract

We prove a Verdier Hypercovering Theorem for cohomology theories arising from motivic spectra. This allows us to construct for smooth quasi-projective complex varieties a natural morphism from etale algebraic to Hodge filtered complex cobordism, which extends the map from etale motivic to Deligne-Beilinson cohomology.