Topological Hochschild homology of maximal orders in simple Q-algebras

Henry Yi-Wei Chan; Ayelet Lindenstrauss

doi:10.2140/agt.2019.19.31

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arXiv · 1505.06385

Topological Hochschild homology of maximal orders in simple Q-algebras

Henry Yi-Wei Chan·Ayelet Lindenstrauss

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Abstract

We calculate the topological Hochschild homology groups of a maximal order in a central 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 THH groups of maximal orders A in simple algebras over Q_p. We show that the topological Hochschild homology of A/(p) splits as the tensor product of its Hochschild homology and the topological Hochschild homology of 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 the homotopy groups of the completion at p of THH(A).

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BibTeX RIS

Henry Yi-Wei Chan, Ayelet Lindenstrauss. 2015-05-23. Topological Hochschild homology of maximal orders in simple Q-algebras. https://doi.org/10.2140/agt.2019.19.31

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