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On the effectivity of spectra representing motivic cohomology theories

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arxiv 1710.00594 v3 pith:O2SPNO5L submitted 2017-10-02 math.KT

Tom Bachmann , Jean Fasel This is my paper · ORCID
classification math.KT
keywords cohomologymotivicspectratheoriescategorycoincideconsequencecriterion
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Let k be an infinite perfect field. We provide a general criterion for a spectrum in the stable homotopy category over k to be effective, i.e. to be in the localizing subcategory generated by the suspension spectra of smooth schemes. As a consequence, we show that two recent versions of generalized motivic cohomology theories coincide.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Modules over algebraic cobordism

    math.AG 2019-08 accept novelty 8.0 of 10

    MGL-modules over a scheme are equivalent to motivic spectra with finite syntomic transfers, and the infinite P^1-loop space of MGL is the A^1-homotopy type of the moduli stack of finite syntomic schemes.

  2. The unit map of the algebraic special linear cobordism spectrum

    math.KT 2019-08 accept novelty 6.0 of 10

    Over characteristic 0 fields, the unit map from the motivic sphere spectrum to the special linear cobordism spectrum MSL is an isomorphism on homotopy modules, proven by comparing framed and SL-oriented framed corresp...

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