论文标题
与椭圆形模块相关的射影分区场的程度界限与无型内态环
Degree bounds for projective division fields associated to elliptic modules with a trivial endomorphism ring
论文作者
论文摘要
令$ k $为全球字段，让$ a $为$ \ text {quet}（a）= k $的deDekind域，让$ k $为有限生成的字段。 Using a unified approach for both elliptic curves and Drinfeld modules $M$ defined over $K$ and having a trivial endomorphism ring, with $k= \mathbb{Q}$, $A = \mathbb{Z}$ in the former case and $k$ a global function field, $A$ its ring of functions regular away from a fixed prime in the latter case, for any nonzero ideal $ \ mathfrak {a} \ lhd a $我们证明了规范$ | \ mathfrak {a} | $的最佳估计，用于$ \ mathfrak {a} $ - $ m $ m $ $ m $ $ m $的$ k $的学位。
Let $k$ be a global field, let $A$ be a Dedekind domain with $\text{Quot}(A) = k$, and let $K$ be a finitely generated field. Using a unified approach for both elliptic curves and Drinfeld modules $M$ defined over $K$ and having a trivial endomorphism ring, with $k= \mathbb{Q}$, $A = \mathbb{Z}$ in the former case and $k$ a global function field, $A$ its ring of functions regular away from a fixed prime in the latter case, for any nonzero ideal $\mathfrak{a} \lhd A$ we prove best possible estimates in the norm $|\mathfrak{a}|$ for the degrees over $K$ of the subfields of the $\mathfrak{a}$-division fields of $M$ fixed by scalars.
