2025/06/12 by Watson, Ryan
#13D07 #13D09 (Primary) 13C40 #16E45 (Secondary) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2506.10757
Given a bounded complex of finitely generated modules M over a commutative noetherian local ring R, one assigns to it a variety, \mathcal VR(M), called the cohomological support variety of M over R. The variety \mathcal VR(M) holds important homological information about the complex and the ring. In this paper, we study the behavior of cohomological support varieties under restriction of scalars along local maps. In the case where the rings involved are complete intersections and the map is a surjective complete intersection, this recovers a theorem of Bergh and Jorgensen. Additionally, we show that if R→ S is a local map of finite flat dimension, then the dimension of \mathcal VR(R) is less than or equal to that of \mathcal VS(S). This allows us to recover Avramov's result that the complete intersection property is preserved under localization.