Barthel, Tobias and Heard, Drew and Naumann, Niko (2022) On conjectures of Hovey-Strickland and Chai. SELECTA MATHEMATICA-NEW SERIES, 28 (3): 56. ISSN 1022-1824, 1420-9020
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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 for Morava E-theory is coherent, and that every finitely generated Morava module can be realized by a K (n)-local spectrum as long as 2p - 2 > n(2) + n. Finally, we deduce consequences of our results for descent of Balmer spectra.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | IWASAWA THEORY; SPECTRA; GEOMETRY; Morava K -theory; Morava modules; Balmer spectrum; Lubin-Tate space; Gross-Hopkins period map |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Niko Naumann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 08 Feb 2024 16:10 |
| Last Modified: | 08 Feb 2024 16:10 |
| URI: | https://pred.uni-regensburg.de/id/eprint/57822 |
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