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01361nam a2200217Ia 4500 |
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10.1007-s00029-022-00766-2 |
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220425s2022 CNT 000 0 und d |
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|a 10221824 (ISSN)
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| 245 |
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|a On conjectures of Hovey–Strickland and Chai
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|b Birkhauser
|c 2022
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|z View Fulltext in Publisher
|u https://doi.org/10.1007/s00029-022-00766-2
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|a 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 2 p- 2 > n2+ n. Finally, we deduce consequences of our results for descent of Balmer spectra. © 2022, The Author(s).
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|a Balmer spectrum
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|a Gross–Hopkins period map
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|a Lubin–Tate space
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|a Morava K-theory
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|a Morava modules
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|a Barthel, T.
|e author
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|a Heard, D.
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|a Naumann, N.
|e author
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| 773 |
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|t Selecta Mathematica, New Series
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