标题： 等变自由分解的对称模序列 显示英文标题

标题： Equivariant Free Resolutions of Sequences of Symmetric Module

摘要： 给定一个相关模的序列$M_n$在一个相关诺特多项式环的序列上，其中每个$M_n$是对称群在$n$个字母上的表示，可以问如何同时计算每个$M_n$的等变自由分解。 在本文中，我们解决了这个问题。 在诺特多项式 FI-代数上的 FI-模设置下，我们提供了一个计算挠率和 FI-等变微分的算法。 作为应用，我们展示了如何使用这个结果来计算在无限多个变量的多项式环中的不变理想等变自由分解的截断，这些理想在严格递增映射的独异半群或排列的作用下是不变的。 这种自由分解中出现的自由模在对称性下是有限生成的。 显示英文摘要

摘要： Given a sequence of related modules $M_n$ over a sequence of related Noetherian polynomial rings, where each $M_n$ is a representation of the symmetric group on $n$ letters, one may ask how to simultaneously compute an equivariant free resolution of each $M_n$. In this article, we address this question. Working in the setting of FI-modules over a Noetherian polynomial FI-algebra, we provide an algorithm for computing syzygies and FI-equivariant differentials. As an application, we show how this result can be used to compute truncations of equivariant free resolutions of ideals in polynomial rings in infinitely many variables that are invariant under actions of the monoid of strictly increasing maps or of permutations. The free modules occurring in such a free resolution are finitely generated up to symmetry.