On conjectures of Hovey–Strickland and Chai

• Tobias Barthel ^[1] ; Drew Heard ^[2] ; Niko Naumann ^[3]
  1. [1] Max Planck Institute for Mathematics

     Max Planck Institute for Mathematics

     Kreisfreie Stadt Bonn, Alemania

     
  2. [2] Norwegian University of Science and Technology

     Norwegian University of Science and Technology

     Noruega

     
  3. [3] University of Regensburg

     University of Regensburg

     Kreisfreie Stadt Regensburg, Alemania

     

  Mostrar afiliaciones +
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 3, 2022
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • We prove the height two case of a conjecture of Hovey and Strickland that provides a K(n)-local analogue of the Hopkins–Smith thick subcategory theorem. Our approach first reduces the general conjecture to a problem in arithmetic geometry posed by Chai.

    We then use the Gross–Hopkins period map to verify Chai’s Hope at height two and all primes. Along the way, we show that the graded commutative ring of completed cooperations forMorava E-theory is coherent, and that every finitely generatedMorava module can be realized by a K(n)-local spectrum as long as 2p −2 > n2 +n. Finally, we deduce consequences of our results for descent of Balmer spectra.