The Dual Motivic Witt Cohomology Steenrod Algebra
Viktor Burghardt

TL;DR
This paper investigates the structure of the dual Steenrod algebra in motivic Witt cohomology, revealing algebraic properties over certain fields and connecting to recent computations of related spectra.
Contribution
It determines the algebra structure of the dual Steenrod algebra for motivic Witt cohomology over specific fields, extending understanding in motivic homotopy theory.
Findings
Computed the algebra structure of ${H_W ext{Z}}_{**}H_W ext{Z}$ over certain fields.
Inverted $ ext{η}$ to analyze the algebra ${HW}_{**}HW$ and related spectra.
Connected results to recent work by Bachmann and Hopkins on $HW$-module structures.
Abstract
In this paper we begin the study of the (dual) Steenrod algebra of the motivic Witt cohomology spectrum by determining the algebra structure of over fields of characteristic not which are extensions of fields with . For example, this includes all fields of odd characteristic, as well as fields that are extensions of quadratically closed fields of characteristic . After inverting , this computes the -algebra . In particular, for the given base fields, this implies the -module structure of recently computed by Bachmann and Hopkins.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Nonlinear Waves and Solitons · Advanced Combinatorial Mathematics
