2023/12/15 by Holanda, Rafael, Miranda-Neto, Cleto B.
#Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2312.09725
We provide a duality theorem between Ext and Tor modules over a Cohen-Macaulay local ring possessing a canonical module, and use it to prove some freeness criteria for finite modules. The applications include a characterization of codimension three complete intersection ideals and progress on a long-held multi-conjecture of Vasconcelos. By a similar technique, we furnish another theorem which in addition makes use of the notion of cohomological dimension and is mainly of interest in dimension one; as an application, we show that the celebrated Huneke-Wiegand conjecture in the case of complete intersections holds true provided that a single additional condition is satisfied.