Does semi-stable reduction behave well with Weil restriction of scalars - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-26T02:57:28Z http://mathoverflow.net/feeds/question/104023 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/104023/does-semi-stable-reduction-behave-well-with-weil-restriction-of-scalars Does semi-stable reduction behave well with Weil restriction of scalars Harry 2012-08-05T14:11:29Z 2012-08-05T14:11:29Z <p>Let $A$ be an abelian variety over a number field $K$ with semi-stable reduction over $O_K$.</p> <p>Does the Weil restriction $\textrm{Res}_{K/\mathbf{Q}}A$ of $A$ to $\mathbf{Q}$ have semi-stable reduction over $\mathbf{Z}$?</p> <p>Note that $\textrm{Res}_{K/\mathbf{Q}}A$ is an abelian variety over $\mathbf{Q}$ of dimension $\dim A \cdot [K:\mathbf{Q}]$.</p>