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arXiv · 2202.11344

The Kakeya conjecture on local fields of positive characteristic

Alejo Salvatore
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Abstract

We state and prove an analogue of the Kakeya conjecture for the local field $\mathbb{F}_q(\!(t)\!)$. This extends Arsovski's result on the Kakeya conjecture to local fields of positive characteristic. We also prove the Kakeya maximal conjecture in this setting.

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Alejo Salvatore. 2022-02-23. The Kakeya conjecture on local fields of positive characteristic. https://arxiv.org/abs/2202.11344

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