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 ${K}_{2n}\left({\mathsc{O}}_{F}\right)$ 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 ${K}_{2n}\left({\mathsc{O}}_{F}\right)$ 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