Bredon motivic cohomology of the real numbers

2024/04/10 by Deng, Bill, Voineagu, Mircea
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2404.06697

Abstract

Over the real numbers with \Z/2-coefficients, we compute the C₂-equivariant Borel motivic cohomology ring, the Bredon motivic cohomology groups and prove that the Bredon motivic cohomology ring of the real numbers is a proper subring in the RO(C₂× C₂)-graded Bredon cohomology ring of a point. This generalizes Voevodsky's computation of the motivic cohomology ring of the real numbers to the C₂-equivariant setting. These computations are extended afterwards to any real closed field.

Related

• Bredon motivic cohomology of the complex numbers
• RO(C₂× C₂)-graded cohomology ring of a point and applications
• About Bredon motivic cohomology of a field
• Topological comparison theorems for Bredon motivic cohomology
• Bigraded Equivariant Cohomology of Real Quadrics