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References (33)
-
A Blumberg, M Mandell (2011)
Derived Koszul duality and involutions in the algebraic K-theory of spacesJ. Topol, 4
-
KT Chen (1971)
Algebras of iterated path integrals and fundamental groupsTrans. AMS, 156
-
V Ginzburg, M Kapranov (1994)
Koszul duality for operads. DukeMath. J, 76
-
A Baker (2012)
On the cohomology of loop spaces for some Thom spaces, New YorkJ. Math, 18
-
JL Loday (2007)
On the algebra of quasi-shufflesManuscripta Math, 123
-
AB Goncharov (2005)
Galois symmetries of fundamental groupoids and noncommutative geometryDuke Math. J, 128
-
W Dwyer, J Greenlees, S Iyengar (2006)
Duality in algebra and topologyAdv. Math, 200
-
D Husemoller, J Moore, J Stasheff (1974)
Differential homological algebra and homogeneous spacesJ. Pure Appl. Algebra, 5
-
M Bökstedt, G Carlsson, R Cohen, T Goodwillie, W-c Hsiang, I Madsen (1996)
On the algebraic K-theory of simply connected spacesDuke. Math. J, 84
-
F Brown (2012)
Mixed Tate motives over [InlineMediaObject not available: see fulltext.]Ann. Math, 175
-
B Fresse (2010)
The bar complex of an E ∞ algebraAdv. Math, 223
-
J Rognes (1994)
The Hatcher-Waldhausen map is a spectrum mapMath. Ann, 299
-
Y Manin (1987)
Remarks on Koszul algebras and quantum groupsAnn. Inst. Fourier (Grenoble), 37
-
S Eilenberg, S Mac Lane (1953)
On the groups of H(π,n) IAnn. of Math., 58
-
M Hazewinkel (2003)
Symmetric functions, noncommutative symmetric functions, and quasisymmetric functions I [& II …]Acta Appl. Math, 75
-
M Atiyah, D Tall (1969)
Group representations, λ-rings and the J-homomorphismTopology, 8
-
P Deligne, A Goncharov (2005)
Groupes fondamentaux motiviques de Tate mixteAnn. Sci. cole Norm. Sup, 38
-
A Borel (1977)
Cohomologie de SL n et valeurs de fonctions zeta aux points entiersAnn. Scuola Norm. Sup. Pisa, 4
-
A Baker, B Richter (2008)
Quasisymmetric functions from a topological point of viewMath. Scand, 103
-
M Hoffmann (2000)
Quasi-shuffle productsJ. Alg. Combin, 11
-
A Beilinson, V Ginzburg, V Schechtman (1988)
Koszul dualityJ. Geom. Phys, 5
-
A Connes, M Marcolli (2006)
Quantum fields and motivesJ. Geom. Phys, 56
-
M Kontsevich (1999)
Operads and motives in deformation quantizationLett. Math. Phys, 48
-
L Smith, RE Stong (1968)
Exotic cobordism theories associated with classical groupsJ. Math. Mech, 17
-
DM Lu, J Palmieri, QS Wu, JJ Zhang (2008)
Koszul equivalences in A ∞ -algebraNew York J. Math, 14
-
JF Adams (1966)
On the groups J(X). IVTopology, 5
-
V Drinfel’d (1991)
On quasitriangular quasi-Hopf algebras and on a group that is closely connected with Gal( Q ¯ / Q $\overline {{\mathbb {Q}}}/{\mathbb {Q}}$ )Leningrad Math. J, 2
-
J Tate (1957)
Homology of Noetherian rings and local ringsIllinois J. Math, 1
-
B Vallette (2008)
Manin products, Koszul duality, Loday algebras and Deligne conjectureJ. Reine Angew. Math, 620
-
K Hess, B Shipley (2014)
The homotopy theory of coalgebras over a comonadProc. Lond. Math. Soc, 108
-
H Bergsaker, J Rognes (2010)
Homology operations in the topological cyclic homology of a pointGeom. Topol, 14
-
A Blumberg, D Gepner, G Tabuada (2013)
A universal characterization of higher algebraic K-theoryGeom. Topol, 17
-
A Blumberg, D Gepner, G Tabuada (2014)
Uniqueness of the multiplicative cyclotomic traceAdv. Math, 260
- Publisher
- Springer Journals
- Copyright
- Copyright © 2015 by Morava.
- Subject
- Mathematics; Mathematics, general; Applications of Mathematics; Computational Mathematics and Numerical Analysis
- eISSN
- 2197-9847
- DOI
- 10.1186/s40687-015-0028-7
- Publisher site
- See Article on Publisher Site
Abstract
Waldhausen’s K-theory of the sphere spectrum (closely related to the algebraic K-theory of the integers) is naturally augmented as an S 0-algebra, and so has a Koszul dual. Classic work of Deligne and Goncharov implies an identification of the rationalization of this (covariant) dual with the Hopf algebra of functions on the motivic group for their category of mixed Tate motives over [InlineMediaObject not available: see fulltext.]. This paper argues that the rationalizations of categories of noncommutative motives defined recently by Blumberg, Gepner, and Tabuada consequently have natural enrichments, with morphism objects in the derived category of mixed Tate motives over [InlineMediaObject not available: see fulltext.]. We suggest that homotopic descent theory lifts this structure to define a category of motives defined not over [InlineMediaObject not available: see fulltext.] but over the sphere ring-spectrum S 0.
Journal
Research in the Mathematical Sciences – Springer Journals
Published: Jun 10, 2015