Spectral Mackey functors and equivariant algebraic K-theory (I)
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Barwick_Spectral Mackey functors.pdf
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556.97 KB
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Author(s)
Barwick, Clark Edward
Date Issued
January 2017
Journal
Advances in Mathematics
Publisher
Elsevier BV
Citation
Barwick, Clark. “Spectral Mackey Functors and Equivariant Algebraic K-Theory (I).” Advances in Mathematics 304 (January 2017): 646–727.
Version
Original manuscript
Abstract
Spectral Mackey functors are homotopy-coherent versions of ordinary Mackey functors as defined by Dress. We show that they can be described as excisive functors on a suitable ∞-category, and we use this to show that universal examples of these objects are given by algebraic K-theory. More importantly, we introduce the unfurling of certain families of Waldhausen ∞-categories bound together with suitable adjoint pairs of functors; this construction completely solves the homotopy coherenc e problem that arises when one wishes to study the algebraic K-theory of such objects as spectral Mackey functors. Finally, we employ this technology to lay the foundations of equivariant stable homotopy theory for profinite groups; the lack of such foundations has been a serious impediment to progress on the conjectures of Gunnar Carlsson. We also study fully functorial versions of A-theory, upside-down A -theory, and the algebraic K-theory of derived stacks.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1016/J.AIM.2016.08.043
