most recent 30 from http://mathoverflow.net 2013-05-23T16:20:30Z http://mathoverflow.net/feeds/user/7060 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/121702/specialization-of-curves-defined-over-function-field wishcow 2013-02-13T11:08:22Z 2013-02-13T12:46:20Z

<p>Let $C$ and $D$ be two algebraic curves defined over a function field $K(t)$ ($K$ is a number field). Suppose that $C$ and $D$ are isomorphic. We can specialize the curves to values in $K$ (nonformally this can be done by just pluggin in a number in $K$ instead of $t$). This scenario is the same as reducing from a generic fiber to a special fiber. Is it true that the specialization of the isomorphism will remain an isomorphism for all but finitely many values in $K$?</p> <p>I am not sure if this is a natural thing to do, or if this is the best way to present the question. I appreciate any help on this.</p>

http://mathoverflow.net/questions/111004/good-reduction-for-singular-varieties wishcow 2012-10-29T15:23:42Z 2012-11-01T21:43:54Z

<p>A projective nonsingular variety $X$ over a number field $K$ has the notion of good reduction at places $p$ of $K$. Informally, $X$ has good reduction modulo $p$ if $X$ remains nonsingular when reduced modulo $p$. A theorem states that for all but finitely many primes we have good reduction (See Hindry and Silverman's "Diophantine Geometry: An Introduction", Proposition A.9.1.6, p.158).</p> <p>Is there a similar notion of good reduction for singular varieties? </p> <p>For example, suppose I have a surface with a single singularity, I expect that for almost all primes the surface will remain "nice" when reduced modulo $p$.</p>

http://mathoverflow.net/questions/72967/is-there-a-magma-function-to-calculate-the-absolutely-irreducible-components-of-a wishcow 2011-08-16T08:44:01Z 2012-03-27T18:43:24Z

<ol> <li><p>Given a curve defined over the rationals, is it computationaly possible to find all its absolutely irreducible components?</p></li> <li><p>Is there an implementation of this in the MAGMA program?</p></li> </ol>

http://mathoverflow.net/questions/14076/irreducibility-of-polynomials-in-two-variables/46029#46029 wishcow 2010-11-14T10:09:30Z 2010-11-14T10:09:30Z

<p>I have a reference for the method mentioned by David Speyer above (sorry couldn't find how to add comment to existing answer):</p> <p>S. Gao, Absolute irreducibility of polynomials via newton polytopes, <a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.5311" rel="nofollow">link</a></p>

http://mathoverflow.net/questions/111004/good-reduction-for-singular-varieties wishcow 2012-10-29T15:50:22Z 2012-10-29T15:50:22Z

Hutz in &quot;Good reduction of periodic points on projective varieties&quot; defines a more general good reduction for a proper scheme over a number field. However, the reduced scheme is still required to be smooth and proper.

http://mathoverflow.net/questions/76352/orthogonal-group-of-quadratic-form wishcow 2012-10-25T17:11:53Z 2012-10-25T17:11:53Z

Do you have a reference for the theorem of Dieudonne?

http://mathoverflow.net/questions/72967/is-there-a-magma-function-to-calculate-the-absolutely-irreducible-components-of-a wishcow 2011-08-17T07:51:06Z 2011-08-17T07:51:06Z

SINGULAR does have an implementation of Gianni/Trager/Zacharias algorithm for absolute prime decomposition.

http://mathoverflow.net/questions/72967/is-there-a-magma-function-to-calculate-the-absolutely-irreducible-components-of-a/72982#72982 wishcow 2011-08-16T16:12:20Z 2011-08-16T16:12:20Z

Thanks for the answer Alvaro, I do not think it answers my question though. Notice that I wrote absolutely irreducible components. For example $x^2+y^2$ is an irreducible component over the rationals, even though it is reducible over the algebraic closure. Magma only checks for the irreducible components and not the absolutely irreducible ones. I will check Sage's function later today.