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August 2022 On the Second Cohomology of the Norm One Group of a p-Adic Division Algebra
Mikhail Ershov
Michigan Math. J. 72: 261-330 (August 2022). DOI: 10.1307/mmj/20217210

Abstract

Let F be a p-adic field, that is, a finite extension of Qp. Let D be a finite dimensional division algebra over F, and let SL1(D) be the group of elements of reduced norm 1 in D. Prasad and Raghunathan proved that H2(SL1(D),R/Z) is a cyclic p-group whose order is bounded from below by the number of p-power roots of unity in F, unless D is a quaternion algebra over Q2. In this paper we give an explicit upper bound for the order of H2(SL1(D),R/Z) for p5 and determine H2(SL1(D),R/Z) precisely when F is cyclotomic, p19, and the degree of D is not a power of p.

Dedication

(with an appendix written by MIKHAIL ERSHOV AND THOMAS WEIGEL)

To Gopal Prasad on the occasion of his 75th birthday

Citation

Download Citation

Mikhail Ershov. "On the Second Cohomology of the Norm One Group of a p-Adic Division Algebra." Michigan Math. J. 72 261 - 330, August 2022. https://doi.org/10.1307/mmj/20217210

Information

Received: 16 April 2021; Revised: 27 September 2021; Published: August 2022
First available in Project Euclid: 2 August 2022

Digital Object Identifier: 10.1307/mmj/20217210

Subjects:
Primary: 20G25
Secondary: 11E72 , 20E18 , 22E41

Rights: Copyright © 2022 The University of Michigan

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Vol.72 • August 2022
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