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Azumaya descent and étale-local cyclotomic comparison: a noncommutative filtration
Bhatt-Morrow-Scholze motivic filtration on topological Hochschild homology ($THH$) is extended to Azumaya algebras over quasisyntomic rings. We prove the Azumaya descent theorem: $THH$ of such an algebra is equivalent, as an underlying spectrum, to $THH$ of its center, normalized on $π_0$ by the
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