most recent 30 from http://mathoverflow.net 2013-06-19T21:40:20Z http://mathoverflow.net/feeds/question/56814 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/56814/cohomology-of-real-algebraic-varieities Colin Tan 2011-02-27T12:50:35Z 2011-02-27T12:50:35Z

<p>I understand Serre's GAGA theorem as saying that equations over algebraically closed fields can be studied equally from the algebraic and analytic points of view, at least with respect to cohomology.</p> <p>Real algebra and real analysis are means to study inequalities over real closed fields. Firstly, I'm wondering if there is a cohomology for real algebraic varieties and real semialgebraic varieties?</p> <p>Given that there is such a cohomology, has there be a comparison of the algebraic cohomology and the analytic cohomology, in analogy to GAGA's theorem? I would expect that if there is such a theorem, it would deny the equivalences of these two approaches. Instead, I would believe that such a theorem would say that algebra can detect strictly less than analysis. For after all, cohomology is about local-global obstructions. </p>