2022/01/18 by Benjamin Briggs, Briggs, Benjamin, Daniel McCormick +3 · 1 citation
Mathematics · #13D02 #13D07 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2201.06762
openalex publication_date 2022/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.