论文标题
潜在的良好减少过椭圆形曲线
Potential good reduction of hyperelliptic curves
论文作者
论文摘要
令$ k $为一个数字字段，$ g \ geq 2 $ a正整数。我们将$ c_k（g）$定义为最小的整数$ n $，因此存在无限的许多$ \ operline {k} $ - 同构的类别$ g $ g $ g $ g $ hyperelliptic curves $ c/k $，所有weiersstrass point in $ k $中的所有weierstrass point in $ k $都具有$ n $ k $的$ n $ primes in $ n $ k $的$ k $。 We show that $c_K(g) > π_{K, \textrm{odd}}(2g) + 1$, where $π_{K, \textrm{odd}}(n)$ denotes the number of odd primes in $K$ with norm no greater than $n$, as well as present a summary of various conditional and unconditional results on upper bounds for $c_K(g)$.
Let $K$ be a number field, and $g \geq 2$ a positive integer. We define $c_K(g)$ as the smallest integer $n$ such that there exist infinitely many $\overline{K}$-isomorphism classes of genus $g$ hyperelliptic curves $C/K$ with all Weierstrass points in $K$ having potentially good reduction outside $n$ primes in $K$. We show that $c_K(g) > π_{K, \textrm{odd}}(2g) + 1$, where $π_{K, \textrm{odd}}(n)$ denotes the number of odd primes in $K$ with norm no greater than $n$, as well as present a summary of various conditional and unconditional results on upper bounds for $c_K(g)$.
