Bunke, Ulrich and Nikolaus, Thomas and Tamme, Georg (2018) The Beilinson regulator is a map of ring spectra. ADVANCES IN MATHEMATICS, 333. pp. 41-86. ISSN 0001-8708, 1090-2082
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We prove that the Beilinson regulator, which is a map from K-theory to absolute Hodge cohomology of a smooth variety, admits a refinement to a map of Em-ring spectra in the sense of algebraic topology. To this end we exhibit absolute Hodge cohomology as the cohomology of a commutative differential graded algebra over R. The associated spectrum to this CDGA is the target of the refinement of the regulator and the usual K-theory spectrum is the source. To prove this result we compute the space of maps from the motivic K-theory spectrum to the motivic spectrum that represents absolute Hodge cohomology using the motivic Snaith theorem. We identify those maps which admit an Em-refinement and prove a uniqueness result for these refinements. (C) 2018 Elsevier Inc. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ALGEBRAIC K-THEORY; INFINITY-CATEGORIES; SPACE; Beilinson regulator; K-theory; Absolute Hodge cohomology; Ring spectra; Motivic homotopy theory |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 12 Feb 2020 13:39 |
| Last Modified: | 12 Feb 2020 13:39 |
| URI: | https://pred.uni-regensburg.de/id/eprint/14199 |
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