@article{861cb2d376a2447786bd2466e555b7af,

title = "Redshift and multiplication for truncated Brown-Peterson spectra",

abstract = "We equip BPhni with an E3-BP-algebra structure for each prime p and height n.The algebraic K-theory of this ring is of chromatic height exactly (Formula Presented)has bounded above fiber.",

keywords = "K-theory, Lichtenbaum-quillen conjecture, Redshift, Topological cyclic homology, Topological hochschild homology, Truncated brown-peterson spectrum",

author = "Jeremy Hahn and Dylan Wilson",

note = "Funding Information: Acknowledgements. We are extremely grateful to the anonymous referees for their careful reading and many helpful comments. The first referee{\textquoteright}s suggestion led to the much simpler proof of the Multiplication Theorem now given in Section 2. The second referee{\textquoteright}s comments inspired us to separate the use of descent and homotopy fixed point spectral sequences in our argument for the Canonical Vanishing Theorem; we hope that our present argument is easier to follow. The third referee{\textquoteright}s comments included many of the results in Section 3 and led to simplifications of several proofs in Section C. The authors are also very grateful to Christian Ausoni, Tyler Lawson, and John Rognes for their comments on an earlier draft. We thank Gabriel Angelini-Knoll, Thomas Nikolaus, Oscar Randal-Williams, and Andrew Salch for useful conversations related to the paper. We are very grateful to Akhil Mathew for stimulating conversations and for permission to include his results in Section 3. We would also like to thank the participants and speakers in Harvard{\textquoteright}s Thursday Seminar in Spring of 2021 for comments, questions, and discussions that helped improve the paper. The first author was supported by NSF grant DMS-1803273, and the second author was supported by NSF grant DMS-1902669. Publisher Copyright: {\textcopyright} 2022 Department of Mathematics, Princeton University.",

year = "2022",

month = nov,

doi = "10.4007/annals.2022.196.3.6",

language = "English (US)",

volume = "196",

pages = "1277--1351",

journal = "Annals of Mathematics",

issn = "0003-486X",

publisher = "Princeton University Press",

number = "3",

}