Kakeya sets over non-archimedean local rings
Abstract
In a recent paper of Ellenberg, Oberlin, and Tao, the authors asked whether there are Besicovitch phenomena in Fq[[t]]n. In this paper, we answer their question in the affirmative by explicitly constructing a Kakeya set in Fq[[t]]n of measure 0. Furthermore, we prove that any Kakeya set in Fq[[t]]2 or Zp2 is of Minkowski dimension 2.
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