## Implicit Function Theorem over arbitrary fields

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 $F_q((1/t))$?

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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