Evil Primes and Superspecial Moduli
| dc.creator | Goren, Eyal Z. | |
| dc.creator | Lauter, Kristin E. | |
| dc.date | 2005-12-20 | |
| dc.date.accessioned | 2026-07-07T06:55:35Z | |
| dc.date.available | 2026-07-07T06:55:35Z | |
| dc.description | For a quartic primitive CM field $K$, we say that a rational prime $p$ is {\it evil} if at least one of the abelian varieties with CM by $K$ reduces modulo a prime ideal $\gerp| p$ to a product of supersingular elliptic curves with the product polarization. We call such primes {\it evil primes for $K$}. In \cite{GL}, we showed that for fixed $K$, such primes are bounded by a quantity related to the discriminant of the field $K$. In this paper, we show that evil primes are ubiquitous in the sense that, for any rational prime $p$, there are an infinite number of fields $K$ for which $p$ is evil for $K$. The proof consists of two parts: (1) showing the surjectivity of the abelian varieties with CM by $K$, for $K$ satisfying some conditions, onto the the superspecial points modulo $\gerp$ of the Hilbert modular variety associated to the intermediate real quadratic field of $K$, and (2) showing the surjectivity of the superspecial points modulo $\gerp$ of the Hilbert modular variety associated to a large enough real quadratic field onto the superspecial points modulo $\gerp$ with principal polarization on the Siegel moduli space. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0512472 | |
| dc.identifier | http://arxiv.org/abs/math/0512472 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106323 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G15; 11G16; 11G18; 11R27 | |
| dc.title | Evil Primes and Superspecial Moduli | |
| dc.type | text |