Milnor excision for motivic spectra

Research output: Contribution to journalJournal articlepeer-review

  • Elden Elmanto
  • Marc Hoyois
  • Ryomei Iwasa
  • Shane Kelly

We prove that the ∞{\infty}-category of motivic spectra satisfies Milnor excision: if A→B{A\to B} is a morphism of commutative rings sending an ideal IA{I\subset A} isomorphically onto an ideal of B, then a motivic spectrum over A is equivalent to a pair of motivic spectra over B and A/I{A/I} that are identified over B/IB{B/IB}. Consequently, any cohomology theory represented by a motivic spectrum satisfies Milnor excision. We also prove Milnor excision for Ayoub's étale motives over schemes of finite virtual cohomological dimension.

Original languageEnglish
JournalJournal fur die Reine und Angewandte Mathematik
Volume2021
Issue number779
Pages (from-to)223-235
ISSN0075-4102
DOIs
Publication statusPublished - 2021

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