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The Cosmic Galois group as Koszul dual to Waldhausen's A(pt)

2011/08/23 by Jack Morava, Morava, Jack
Mathematics · #11G #19F #57R #81T #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:11G #msc:19F #msc:57R #msc:81T

paper · pdf · doi:10.48550/arxiv.1108.4627

Notes from a talk at the Hamburg August 2011 conference http://www.math.uni-hamburg.de/home/richter/hh2011.html on structured ring spectra

arxiv created 2011/08/23 · openalex publication_date 2011/08/23 · arxiv updated 2011/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

K. Hess's theory of homotopical descent, applied to the large categories of motives defined recently by Blumberg, Gepner, and Tabuada, suggests that the Koszul dual of Waldhausen's K-theory of the sphere spectrum, regarded as a supplemented algebra via the Dennis trace, plays a very general role as a kind of motivic group. After tensoring with the rationals, the resulting Hopf algebra has close relations to the ring of quasi-symmetric functions and work of Baker and Richter on one hand, and on the other to work of Deligne and others on the motivic group for mixed Tate motives.

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