论文标题
当地代数中的辅助跳跃基因座和二元性
Cohomological jump loci and duality in local algebra
论文作者
论文摘要
在本文中，在局部DG代数的Koszul扩展上引入并研究了一个名为“共同跳跃基因座”的高阶支持理论，称为“共同体跳跃基因座”。此设置的通用性适用于局部完整的交叉环，外部代数和某些组代数的DG模块。在每种情况下，这个品种家族都概括了研究良好的支持品种。我们表明，共同的跳跃基因座满足了几个有趣的属性，包括在（Grothendieck）双重性下关闭。该支持理论的主要应用是，在局部环上，贝蒂（Betti）程度和复杂性的同源性不变性在二元性下保留，用于有限生成的具有有限的完全相交维度的有限生成的模块。
In this article a higher order support theory, called the cohomological jump loci, is introduced and studied for dg modules over a Koszul extension of a local dg algebra. The generality of this setting applies to dg modules over local complete intersection rings, exterior algebras and certain group algebras in prime characteristic. This family of varieties generalizes the well-studied support varieties in each of these contexts. We show that cohomological jump loci satisfy several interesting properties, including being closed under (Grothendieck) duality. The main application of this support theory is that over a local ring the homological invariants of Betti degree and complexity are preserved under duality for finitely generated modules having finite complete intersection dimension.
