Bunke, Ulrich ; Nikolaus, Thomas ; Tamme, Georg
Alternative Links zum Volltext:DOIVerlag
| Dokumentenart: | Artikel |
|---|
| Titel eines Journals oder einer Zeitschrift: | Advances in Mathematics |
|---|
| Verlag: | ACADEMIC PRESS INC ELSEVIER SCIENCE |
|---|
| Ort der Veröffentlichung: | SAN DIEGO |
|---|
| Band: | 333 |
|---|
| Seitenbereich: | S. 41-86 |
|---|
| Datum: | 2018 |
|---|
| Institutionen: | Mathematik |
|---|
| Identifikationsnummer: | | Wert | Typ |
|---|
| 10.1016/j.aim.2018.05.027 | DOI |
|
|---|
| Stichwörter / Keywords: | ALGEBRAIC K-THEORY; INFINITY-CATEGORIES; SPACE; Beilinson regulator; K-theory; Absolute Hodge cohomology; Ring spectra; Motivic homotopy theory |
|---|
| Dewey-Dezimal-Klassifikation: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
|---|
| Status: | Veröffentlicht |
|---|
| Begutachtet: | Ja, diese Version wurde begutachtet |
|---|
| An der Universität Regensburg entstanden: | Ja |
|---|
| Dokumenten-ID: | 46973 |
|---|
Zusammenfassung
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 ...
Zusammenfassung
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.
Altmetric