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Preprint Number 1660
1660. Will Johnson Dp-finite fields II: the canonical topology and its relation to henselianity E-mail: Submission date: 14 October 2019 Abstract: We continue our earlier investigation of dp-finite fields. We show that the heavy sets of [5] are exactly the sets of full dp-rank. As a consequence, full dp-rank is a definable property in definable families of sets. If $I$ is the group of infinitesimals, we show that $1 + I$ is the group of multiplicative infinitesimals. From this, we deduce that the canonical topology is a field topology. Lastly, we consider the (unlikely) conjecture that the canonical topology is a V-topology. Assuming this conjecture, we deduce the classification of dp-finite fields conjectured by Halevi, Hasson, and Jahnke. Mathematics Subject Classification: Keywords and phrases: |
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