265 citations · 300 across the 15 of their papers we have counts for
14 papers · 1 filter
On the matlis duals of local cohomology modules
Gennady Lyubeznik, Tuğba Yıldırım
Let be a Noetherian regular local ring containing a field of characteristic and a nonzero ideal of . In this short note, we prove that if $\operator…
An extension of a theorem of Hartshorne
Mordechai Katzman, Gennady Lyubeznik, Wenliang Zhang
We extend a classical theorem of Hartshorne concerning the connectedness of the punctured spectrum of a local ring by analyzing the homology groups of a simplicial complex associat…
Local cohomology modules supported at determinantal ideals
Gennady Lyubeznik, Anurag K. Singh, Uli Walther
We provide new results on the vanishing of local cohomology modules supported at ideals of minors of matrices over arbitrary commutative Noetherian rings. In the process, we comput…
Local cohomology modules of a smooth Z-algebra have finitely many associated primes
Bhargav Bhatt, Manuel Blickle, Gennady Lyubeznik +2
Let be a commutative Noetherian ring that is a smooth -algebra. For each ideal of and integer , we prove that the local cohomology module has f…
Two interesting examples of -modules in characteristic
Mordechai Katzman, Gennady Lyubeznik, Wenliang Zhang
We provide two examples of -modules in prime characteristic which answer two open problems in \cite{Lyubeznik} in the negative.
An upper bound on the number of F-jumping coefficients of a principal ideal
Mordechai Katzman, Gennady Lyubeznik, Wenliang Zhang
We prove a result relating the Jacobian ideal and the generalized test ideal associated to a principal ideal in with or in …