MathDB

Henselianity conjecture for NIP valued fields

Let (K,O)(K,\mathcal{O}) be an NIP valued field, where O\mathcal{O} is its valuation ring.

Henselianity conjecture. The valuation ring O\mathcal{O} is henselian.

The source notes that NIP valued fields of positive characteristic are known to be henselian and proposes this stronger statement for arbitrary NIP valued fields.

Equivalent formulations 1

Other statements of this same problem, merged from separate entries. Each is equivalent to the statement above — proving any one settles them all.

  1. The henselianity conjecture for NIP valued fields

    Let (K,v)(K,v) be an NIP valued field. Henselianity conjecture. Every NIP valued field (K,v)(K,v) is henselian. This is one of the main conjectures on NIP fields and would constrain the valuation-theoretic structure of such fields; its resolution status is not specified in the source.

    source: Will Johnson, “Dp-finite fields V: topological fields of finite weight”, arXiv:2004.14732 (2020).

Sources & referencesView supporting material

Primary source

Will Johnson, “Dp-finite fields II: the canonical topology and its relation to henselianity”, arXiv:1910.05932 (2019).

henselianitymodel-theorynip-theoryvalued-fields

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.