most recent 30 from http://mathoverflow.net 2013-05-23T07:42:14Z http://mathoverflow.net/feeds/question/58291 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/58291/riemann-roch-for-arbitrary-function-fields Jizhan Hong 2011-03-12T21:39:54Z 2011-03-12T21:39:54Z

<p>I know that on an algebraic function field in one variable over any base field, there is a good divisor theory for it and a Riemann-Roch Theorem; in particular, there is a 'good' notion of 'genus'. (Which, I guess, is in general different from the corresponding notions in the geometric sense.) References are e.g. Chevalley's book and Deuring's book on algebraic function field in one variable, and Fried&amp;Jarden's "Field Arithmetic".</p> <p>Is there a generalization of these things to an arbitrary function field, which is of arbitrary transcendental degree over an arbitrary base field? Thanks!</p>