Free Incomplete Tambara Functors are Almost Never Flat

Michael A. Hill, David Mehrle, James D. Quigley

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Free algebras are always free as modules over the base ring in classical algebra. In equivariant algebra, free incomplete Tambara functors play the role of free algebras and Mackey functors play the role of modules. Surprisingly, free incomplete Tambara functors often fail to be free as Mackey functors. In this paper, we determine for all finite groups conditions under which a free incomplete Tambara functor is free as a Mackey functor. For solvable groups, we show that a free incomplete Tambara functor is flat as a Mackey functor precisely when these conditions hold. Our results imply that free incomplete Tambara functors are almost never flat as Mackey functors. However, we show that after suitable localizations, free incomplete Tambara functors are always free as Mackey functors.

Original languageEnglish (US)
Pages (from-to)4225-4291
Number of pages67
JournalInternational Mathematics Research Notices
Volume2023
Issue number5
DOIs
StatePublished - Mar 1 2023
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2021 The Author(s). Published by Oxford University Press. All rights reserved.

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