Notes on Milnor-Witt K-theory

2023/05/29 by Déglise, Frédéric · 2 citations
#11E04 #11E39 #11E81 #14F42 #16S10 #19D45 #19E99 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2305.18609

Abstract

These notes develop the foundations of Milnor-Witt K-theory for fields of arbitrary characteristic, without any perfectness assumptions. Extending the work of Morel and Feld, we establish all functorial properties of Milnor-Witt K-theory with careful attention to twists. A main new contribution is the computation of transfers in the general, in particular inseparable, case using Grothendieck (differential) trace maps. The results provide a complete framework for the functoriality axioms of Milnor-Witt modules and form the basis for an upcoming work on Chow-Witt groups with Niels Feld and Fangzhou Jin.

Cited by

• Monadic resolutions for generalized spaces
• Relative \mathbbA¹-Contractibility of Koras-Russell Prototypes and Exotic Motivic Spheres

Related

• Milnor-Witt K-theory and Witt K-theory of a field
• Transfers on Milnor-Witt K-theory
• Periodicity of hermitian K-theory and Milnor's K-groups
• The Milnor-Chow homomorphism revisited
• Lectures on Chow-Witt groups