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2019 Topological Hochschild homology of maximal orders in simple $\mathbb{Q}$–algebras
Henry Yi-Wei Chan, Ayelet Lindenstrauss
Algebr. Geom. Topol. 19(1): 31-75 (2019). DOI: 10.2140/agt.2019.19.31

Abstract

We calculate the topological Hochschild homology groups of a maximal order in a simple algebra over the rationals. Since the positive-dimensional THH groups consist only of torsion, we do this one prime ideal at a time for all the nonzero prime ideals in the center of the maximal order. This allows us to reduce the problem to studying the topological Hochschild homology groups of maximal orders A in simple p –algebras. We show that the topological Hochschild homology of A ( p ) splits as the tensor product of its Hochschild homology with THH ( F p ) . We use this result in Brun’s spectral sequence to calculate THH ( A , A ( p ) ) , and then we analyze the torsion to get π ( THH ( A ) p ) .

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Henry Yi-Wei Chan. Ayelet Lindenstrauss. "Topological Hochschild homology of maximal orders in simple $\mathbb{Q}$–algebras." Algebr. Geom. Topol. 19 (1) 31 - 75, 2019. https://doi.org/10.2140/agt.2019.19.31

Information

Received: 24 June 2015; Revised: 4 February 2018; Accepted: 5 August 2018; Published: 2019
First available in Project Euclid: 12 February 2019

zbMATH: 07053570
MathSciNet: MR3910577
Digital Object Identifier: 10.2140/agt.2019.19.31

Subjects:
Primary: 16E40, 19D55
Secondary: 16H10, 55T99

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.19 • No. 1 • 2019
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