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We continue our earlier investigation of dp-finite fields. We show that the"heavy sets" of [6] are exactly the sets of full dp-rank. As a consequence,full dp-rank is a definable property in definable families of sets. If $I$ isthe group of infinitesimals, we show that $1 + I$ is the group ofmultiplicative infinitesimals. From this, we deduce that the canonical topologyis a field topology. Lastly, we consider the (unlikely) conjecture that thecanonical topology is a V-topology. Assuming this conjecture, we deduce theclassification of dp-finite fields conjectured by Halevi, Hasson, and Jahnke.

Dp-finite fields II: the canonical topology and its relation to henselianity