most recent 30 from http://mathoverflow.net 2013-05-24T11:32:20Z http://mathoverflow.net/feeds/question/110295 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/110295/research-in-algebraic-geometry-involving-filters six 2012-10-22T03:28:46Z 2012-10-22T17:52:18Z

<p>In Gillman and Jerrison's book, "Rings of Continuous Functions", they show a nice relationship between the set of z-ideals in C(X) and the set of filters on X. One can go for with this relationship; for example, proving the smallest measurable cardinal (if any exist) is strongly inaccessible, seems to be better understood from a filter perspective (rather than ideal). </p> <p>Now instead of considering the spectrum of a ring, is there any usefulness to consider the set of filters (which consist of algebraic sets), and defining a topology on it? It just seems like some things (like analytic stuff) would be more natural working in a filter setting.</p> <p>I suppose for a variety V, you could work with something like Filt(V) instead of Spec(V). Where Filt(V) consists of fixed filters of a certain type (each filter would correspond to a variety). Is there any study of this kind? Or is this analogy not very useful? </p>