Borel isomorphism and absolute purity

2019/02/06 by Frédéric Déglise, Jean Fasel, Déglise, Frédéric +6 · 2 citations
Chemistry · Mathematics · #11E81) #14C35 (11E70 #14F42 #19G38 #19L10 #Absolute (philosophy) #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Chemistry #Crystallography #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Isomorphism (crystallography) #Mathematics #Philosophy #Theology #math.AG #msc:14C35 #msc:14F42 #msc:19G38 #msc:19L10

paper · pdf · doi:10.48550/arxiv.1902.02055

published in arXiv (Cornell University) (Cornell University)

arxiv created 2019/02/06 · openalex publication_date 2019/02/06 · arxiv updated 2019/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove absolute purity for the rational motivic sphere spectrum. The main ingredient is the construction of an analogue of the Chern character, where algebraic K-theory is replaced by hermitian K-theory, and motivic cohomology by the plus and minus parts of the rational sphere spectrum. Another ingredient is absolute purity for hermitian K-theory.

Citations

• On the motivic commutative ring spectrum BO
• Slices of hermitian K–theory and Milnor’s conjecture on quadratic forms
• Fundamental classes in motivic homotopy theory

Related

• Chern classes, K-theory and Landweber exactness over nonregular base schemes
• A motivic analogue of the K(1)-local sphere spectrum
• The Borel character
• A motivic spectrum representing hermitian K-theory
• A cellular absolute motivic ring spectrum representing Hermitian K-theory