On numerical equivalence for algebraic cobordism

Cited 1 time in webofscience Cited 0 time in scopus
  • Hit : 509
  • Download : 0
We define and study the notion of numerical equivalence on algebraic cobordism cycles. We prove that algebraic cobordism modulo numerical equivalence is a finitely generated module over the Lazard ring, and it reproduces the Chow group modulo numerical equivalence. We show this theory defines an oriented Borel-Moore homology theory on schemes and oriented cohomology theory on smooth varieties. We compare it with homological equivalence and smash-equivalence for cobordism cycles. For the former, we show that homological equivalence on algebraic cobordism is strictly finer than numerical equivalence, answering negatively the integral cobordism analogue of the standard conjecture (D). For the latter, using Kimura finiteness on cobordism motives, we partially resolve the cobordism analogue of a conjecture by Voevodsky on rational smash-equivalence and numerical equivalence.
Publisher
ELSEVIER SCIENCE BV
Issue Date
2016-01
Language
English
Article Type
Article
Citation

JOURNAL OF PURE AND APPLIED ALGEBRA, v.220, no.1, pp.435 - 464

ISSN
0022-4049
DOI
10.1016/j.jpaa.2015.07.002
URI
http://hdl.handle.net/10203/205998
Appears in Collection
MA-Journal Papers(저널논문)
Files in This Item
There are no files associated with this item.
This item is cited by other documents in WoS
⊙ Detail Information in WoSⓡ Click to see webofscience_button
⊙ Cited 1 items in WoS Click to see citing articles in records_button

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0