Geodesic
Operational $K$-theory
Documenta mathematica, Tome 20 (2015), pp. 357-399
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We study the operational bivariant theory associated to the covariant theory of Grothendieck groups of coherent sheaves, and prove that it has many geometric properties analogous to those of operational Chow theory. This operational K-theory agrees with Grothendieck groups of vector bundles on smooth varieties, admits a natural map from the Grothen­dieck group of perfect complexes on general varieties, satisfies descent for Chow envelopes, and is A1-homotopy invariant.
DOI : 10.4171/dm/493
Classification : 14C15, 14C35, 14L30, 14M25, 19E08 
@article{10_4171_dm_493,
     author = {Sam Payne and Dave Anderson},
     title = {Operational $K$-theory},
     journal = {Documenta mathematica},
     pages = {357--399},
     year = {2015},
     volume = {20},
     doi = {10.4171/dm/493},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/493/}
}
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Sam Payne; Dave Anderson. Operational $K$-theory. Documenta mathematica, Tome 20 (2015), pp. 357-399. doi: 10.4171/dm/493

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