Vol. 2, No. 2, 2020

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Statistics of $K$-groups modulo $p$ for the ring of integers of a varying quadratic number field

Bruce W. Jordan, Zev Klagsbrun, Bjorn Poonen, Christopher Skinner and Yevgeny Zaytman

Vol. 2 (2020), No. 2, 287–307
Abstract

For each odd prime p, we conjecture the distribution of the p-torsion subgroup of K2n(OF) as F ranges over real quadratic fields, or over imaginary quadratic fields. We then prove that the average size of the 3-torsion subgroup of K2n(OF) is as predicted by this conjecture.

Keywords
algebraic K-theory, ring of integers, class group, Cohen-Lenstra heuristics
Mathematical Subject Classification 2010
Primary: 11R70
Secondary: 11R29, 19D50, 19F99
Milestones
Received: 21 June 2018
Revised: 27 January 2019
Accepted: 12 March 2019
Published: 2 August 2019
Authors
Bruce W. Jordan
Department of Mathematics
Baruch College, City University of New York
New York, NY
United States
Zev Klagsbrun
Center for Communications Research
San Diego, CA
United States
Bjorn Poonen
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States
Christopher Skinner
Department of Mathematics
Princeton University
Princeton, NJ
United States
Yevgeny Zaytman
Center for Communications Research
Princeton, NJ
United States