On class numbers of division fields of abelian varieties
作者: Jędrzej Garnek
刊名: Journal de théorie des nombres de Bordeaux, 2019, Vol.31 (1), pp.227-242
来源数据库: The Center for Diffusion of Academic Mathematical Journals
DOI: 10.5802/jtnb.1077
关键词: Division fieldsClass numberAbelian varieties
原始语种摘要: Let $A$ be an abelian variety defined over a number field $K$. Fix a prime $p$ and a natural number $n$ and consider the field $K_n$, obtained by adjoining to $K$ all the coordinates of the $p^n$-torsion points of $A$. We give a lower bound on the $p$-part of the class group of $K_n$ for large $n$, by finding a large unramified extension of $K_n$. This lower bound depends on the Mordell–Weil rank of $A$ and the reduction of $p$-torsion points modulo primes above $p$.
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  •  划分
  • unramified 非分歧的
  • torsion 扭转
  • modulo 
  • class 
  • numbers 数目
  • adjoining 并列
  • large 大的
  • bound 
  • Division 划分
  • division 划分