A Hochschild-cyclic approach to additive higher Chow cycles

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dc.creatorPark, Jinhyun
dc.date2008-02-14
dc.date.accessioned2026-07-07T09:20:44Z
dc.date.available2026-07-07T09:20:44Z
dc.descriptionOver a field of characteristic zero, we introduce two motivic operations on additive higher Chow cycles: analogues of the Connes boundary $B$ operator and the shuffle product on Hochschild complexes. The former allows us to apply the formalism of mixed complexes to additive Chow complexes building a bridge between additive higher Chow theory and additive $K$-theory. The latter induces a wedge product on additive Chow groups for which we show that the Connes operator is a graded derivation for the wedge product using a variation of a Totaro's cycle. Hence, the additive higher Chow groups with the wedge product and the Connes operator form a commutative differential graded algebra. On zero-cycles, they induce the wedge product and the exterior derivation on the absolute Kähler differentials, answering a question of S. Bloch and H. Esnault.
dc.description25 pages
dc.identifierhttps://arxiv.org/abs/0802.1964
dc.identifierhttp://arxiv.org/abs/0802.1964
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/154814
dc.subjectAlgebraic Geometry
dc.subjectK-Theory and Homology
dc.subject19E15, 16E40
dc.titleA Hochschild-cyclic approach to additive higher Chow cycles
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