论文标题
具有额外内态性的某些品种的普通素数
Ordinary primes for some varieties with extra endomorphisms
论文作者
论文摘要
让A为在数字字段和尺寸g上定义的Abelian品种。当G <3（按最近的Sawin工作）时，我们知道一组普通素的密度的确切（非零）值。我们表明，如果g = 3并且a通过假想的二次场E具有乘法，则存在非零的普通素数的非零密度集。当G = 3并通过完全真实的立方场乘法时，我们还会获得部分结果。我们表明，我们的方法还适用于某些Albert IV型的Abelian品种，具有更高的维度。这些结果来自Katz，Ogus和Serre的L-ADIC方法的扩展版，在存在额外的内态性的情况下。
Let A be an abelian variety defined over a number field and of dimension g. When g<3, by the recent work of Sawin, we know the exact (nonzero) value of the density of the set of primes which are ordinary for A. In higher dimension very little is known. We show that if g=3 and A has multiplication by an imaginary quadratic field E, then there exists a nonzero density set of ordinary primes for A. We reach the same conclusion if g=4 and the pair (A,E) has signature (2,2). We also obtain partial results when g=3 and A has multiplication by a totally real cubic field. We show that our methods also apply to certain abelian varieties of Albert type IV of higher dimension. These results are derived from an extended version of the l-adic methods of Katz, Ogus, and Serre in the presence of extra endomorphisms.
