Implicit Function Theorem over arbitrary fields - MathOverflow most recent 30 from http://mathoverflow.net2013-05-24T22:16:43Zhttp://mathoverflow.net/feeds/question/60089http://www.creativecommons.org/licenses/by-nc/2.5/rdfhttp://mathoverflow.net/questions/60089/implicit-function-theorem-over-arbitrary-fieldsImplicit Function Theorem over arbitrary fieldsAlan Lee2011-03-30T17:03:13Z2011-03-30T18:02:20Z
<p>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 $F_q((1/t))$?</p>
http://mathoverflow.net/questions/60089/implicit-function-theorem-over-arbitrary-fields/60098#60098Answer by Anatoly Kochubei for Implicit Function Theorem over arbitrary fieldsAnatoly Kochubei2011-03-30T18:02:20Z2011-03-30T18:02:20Z<p>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.</p>