Sign up ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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 $F_q((1/t))$?

share|cite|improve this question
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 '11 at 17:22

1 Answer 1

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.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.