ON THE STEENROD MODULE STRUCTURE OF ℝ-MOTIVIC SPANIER-WHITEHEAD DUALS

Prasit Bhattacharya; Bertrand J. Guillou; Ang Li

doi:10.1090/bproc/227

ON THE STEENROD MODULE STRUCTURE OF ℝ-MOTIVIC SPANIER-WHITEHEAD DUALS

Prasit Bhattacharya, Bertrand J. Guillou, Ang Li

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The ℝ-motivic cohomology of an ℝ -motivic spectrum is a module over the R-motivic Steenrod algebra A^ℝ. In this paper, we describe how to recover the ℝ -motivic cohomology of the Spanier–Whitehead dual DX of an ℝ -motivic finite complex X, as an A^ℝ-module, given the A^ℝ -module structure on the cohomology of X. As an application, we show that 16 out of 128 different A^ℝ-module structures on A^ℝ(1):= 〈Sq¹, Sq²〉 are self-dual.

Original language	English
Pages (from-to)	555-569
Number of pages	15
Journal	Proceedings of the American Mathematical Society, Series B
Volume	11
Issue number	1
DOIs	https://doi.org/10.1090/bproc/227
State	Published - 2024

Bibliographical note

Publisher Copyright:
© 2024 by the author(s).

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology
Discrete Mathematics and Combinatorics

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abstract = "The ℝ-motivic cohomology of an ℝ -motivic spectrum is a module over the R-motivic Steenrod algebra Aℝ. In this paper, we describe how to recover the ℝ -motivic cohomology of the Spanier–Whitehead dual DX of an ℝ -motivic finite complex X, as an Aℝ-module, given the Aℝ -module structure on the cohomology of X. As an application, we show that 16 out of 128 different Aℝ-module structures on Aℝ(1):= 〈Sq1, Sq2〉 are self-dual.",

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ON THE STEENROD MODULE STRUCTURE OF ℝ-MOTIVIC SPANIER-WHITEHEAD DUALS

Abstract

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