发表机构
UFF（联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究引入复环面同态的类型概念，证明其性质并给出确定同态核、计算同源逆类型等的有效方法。
AI 中文摘要
利用整数矩阵的行列式因子，即固定阶子式的最大公约数，我们引入复环面同态$f$的类型概念，其与极化的类型类似。我们证明该类型在与同构复合时保持不变，且能完全将$f$的核描述为群；更确切地说，核关于其含0的连通分支的商是循环群的乘积，其阶由$f$的类型决定。由于该类型可从$f$的任意有理表示计算得到，这为确定同态的核提供了有效方法。作为推论，当$f$具有有限核时，我们计算其经典不变量次数与指数；当$f$为同源时，还可从$f$的类型计算其逆同源的类型；最后，我们比较极化的类型与其关联同源的类型。
英文摘要
Using determinantal divisors of integral matrices, that is, greatest common divisors of minors of fixed order, we introduce the notion of type of a homomorphism $f$ of complex tori, which is similar to the type of a polarization. We show that the type is invariant under composition with isomorphisms, and that it completely describes the kernel of $f$ as a group. More precisely, the quotient of the kernel by its connected component containing 0 is a product of cyclic groups whose orders are determined by the type of $f$. Since the type can be computed from any rational representation of $f$, this gives an effective way to determine the kernel of a homomorphism. As a consequence, we compute the classic invariants degree and exponent of $f$, when $f$ has finite kernel. When $f$ is an isogeny, we also compute the type of its inverse isogeny from that of $f$. Finally, we compare the type of a polarization to the type of its associated isogeny.
Comments9 pages
