Local cohomology and Gorenstein injective dimension over local homomorphisms
Leila Khatami, Massoud Tousi, Siamak Yassemi
Abstract
A generalization of Grothendieck's non-vanishing theorem is proved for a module which is finite over a local homomorphism. It is also proved that the Gorenstein injective dimension of such a module, if finite, is bounded below by its Krull dimension and is equal to the supremum of the depths of the localizations of the ring over primes in the support of the module.
Create a lesson
Related papers
On the weak Lefschetz property of Artinian Gorenstein algebras of codimension three in arbitrary characteristic
Omkar Javadekar
Linear Independence of Polynomial Compositions and Identifiability of Deep Neural Networks
Kathlén Kohn, Giovanni Luca Marchetti, Alex Massarenti et al.
Comparing v-numbers of symbolic and ordinary powers of squarefree monomial ideals
Trung Chau, Tài Huy Hà, A. V. Jayanthan et al.
Polynomial extensions do not preserve the strong finite type property
Viet-Hoang Tran, Phan Thanh Toan, Thieu N. Vo et al.
Reduction numbers for witnesses to the generalized Loewy length
Richard Bartels, Sarah Dajani, Gabriel Koomson
Multi-graded generic initial ideals, regularity, and the optimal colorful fractional Helly theorem for d-Leray complexes
Daniel McGinnis