Hilbert, the nullstellensatz, and algebraic number theory - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-21T20:47:11Z http://mathoverflow.net/feeds/question/58503 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/58503/hilbert-the-nullstellensatz-and-algebraic-number-theory Hilbert, the nullstellensatz, and algebraic number theory teil 2011-03-15T04:15:44Z 2011-03-15T09:40:08Z <p>I read that Hilbert used the nullstellensatz in algebraic number theory rather than in algebraic geometry. What did he use it for? Today, is the nullstellensatz used in algebraic number theory or other areas apart from algebraic geometry?</p> http://mathoverflow.net/questions/58503/hilbert-the-nullstellensatz-and-algebraic-number-theory/58514#58514 Answer by quid for Hilbert, the nullstellensatz, and algebraic number theory quid 2011-03-15T09:40:08Z 2011-03-15T09:40:08Z <p>I answer: 'is the Nullstellensatz used in other areas?'</p> <p>Yes, for example, a variant is used in Combinatorics.</p> <p>There is a Combinatorial Nullstellensatz (due to N. Alon). The rough idea is to translate certain combinatorial problems into statements on the (non-)vanishing of systems of polynomial equations, and then to analyse this system of polynomial equations.</p> <p>A <a href="http://mathoverflow.net/questions/43317/how-to-recognise-that-the-polynomial-method-might-work" rel="nofollow">question</a> related to it was somewhat recently asked on this site by gowers where you can find details on it. </p>