Geodesic
Connective $K$-theory and Adams operations
Olivier Haution1 ; Alexander Merkurjev2 orcid
1Ludwig-Maximilians-Universität München, Germany
2University of California, Los Angeles, USA
EMS surveys in mathematical sciences, Tome 8 (2021), pp. 135-162

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DOI

We investigate the relations between the Grothendieck group of coherent modules of an algebraic variety and its Chow group of algebraic cycles modulo rational equivalence. Those are in essence torsion phenomena, which we attempt to control by considering the action of the Adams operations on the Brown–Gersten–Quillen spectral sequence and related objects, such as connective K0​-theory. We provide elementary arguments whenever possible. As applications, we compute the connective K0​-theory of the following objects: (1) the variety of reduced norm one elements in a central division algebra of prime degree; (2) the classifying space of the split special orthogonal group of odd degree.
DOI : 10.4171/emss/50
Classification : 19-XX
Mots-clés : Connective K-theory, Adams operations, Chow groups

Olivier Haution  1   ; Alexander Merkurjev  2

1 Ludwig-Maximilians-Universität München, Germany
2 University of California, Los Angeles, USA 
Olivier Haution; Alexander Merkurjev. Connective $K$-theory and Adams operations. EMS surveys in mathematical sciences, Tome 8 (2021), pp. 135-162. doi: 10.4171/emss/50
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     title = {Connective $K$-theory and {Adams} operations},
     journal = {EMS surveys in mathematical sciences},
     pages = {135--162},
     year = {2021},
     volume = {8},
     doi = {10.4171/emss/50},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/emss/50/}
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