Kakeya sets over non-archimedean local rings

Details Kakeya sets over non-archimedean local rings Kakeya sets over non-archimedean local rings

2011-12-14

arxiv.org/abs/1112.3381v1

Mathematics

Combinatorics

10 pages

Scientific paper

In a recent paper of Ellenberg, Oberlin, and Tao, the authors asked whether
there are Besicovitch phenomena in F_q[[t]]^n. In this paper, we answer their
question in the affirmative by explicitly constructing a Kakeya set in
F_q[[t]]^n of measure 0. Furthermore, we prove that any Kakeya set in
F_q[[t]]^2 or Z_p^2 is of Minkowski dimension 2.

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