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Are there any restrictions on the ground field over which the implicit function theorem holds? In particular, does the theorem hold over function fields like $F_q((1/t))$?

flag	asked Mar 30 2011 at 17:03 Alan Lee 11●1

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The field $\mathbb{F}_q((1/t))$ is not a "function field", at least not according to my philosophy. Perhaps you could specify what you mean by a function field and also what statement counts as "the implicit function theorem" over your function fields? – Pete L. Clark Mar 30 2011 at 17:22

Anatoly Kochubei · Answer 1 · 2011-03-30 18:02:20Z UTC

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There is an implicit function theorem valid for any non-Archimedean field. See Theorem 2.2.1 in J.-I. Igusa, An introduction to the theory of local zeta functions. AMS, 2000.

answered Mar 30 2011 at 18:02

Anatoly Kochubei
3,072●1●4●9

Implicit Function Theorem over arbitrary fields

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