On exact ∞-categories and the Theorem of the Heart
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Barwick_On exact.pdf
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284.84 KB
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Author(s)
Barwick, Clark Edward
Date Issued
August 2015
Journal
Compositio Mathematica
Publisher
Cambridge University Press
Citation
Barwick, Clark. “On exact ∞-categories and the Theorem of the Heart.” Compositio Mathematica, vol. 151, no. 11, 2015, pp. 2160–2186.
Version
Original manuscript
Abstract
The new homotopy theory of exact∞-categories is introduced and employed to prove a Theorem of the Heart for algebraic K-theory (in the sense of Waldhausen). This implies a new compatibility between Waldhausen KK-theory and Neeman K-theory. Additionally, it provides a new proof of the Dévissage and Localization theorems of Blumberg–Mandell, new models for the G-theory of schemes, and a proof of the invariance of G-theory under derived nil-thickenings.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1112/S0010437X15007447
