68 citations · 258 across the 40 of their papers we have counts for
12 papers · 1 filter
The arithmetic rank of determinantal nullcones
Jack Jeffries, Vaibhav Pandey, Anurag K. Singh +1
We compute the arithmetic rank as well as the local/étale cohomological dimension of nullcone ideals arising from the classical actions of the symplectic group, the general linear…
On the natural nullcones of the symplectic and general linear groups
Vaibhav Pandey, Yevgeniya Tarasova, Uli Walther
Consider a group acting on a polynomial ring S over a field K by degree-preserving K-algebra automorphisms. Several key properties of the invariant ring can be deduced by studying…
Local cohomology -- an invitation
Uli Walther, Wenliang Zhang
This article is part introduction and part survey to the mathematical area centered around local cohomology.
Koszul and local cohomology, and a question of Dutta
Linquan Ma, Anurag K. Singh, Uli Walther
For a local ring of dimension , we study the natural map from the Koszul cohomology module to the local cohomology module $H^n_\mathfra…
On a conjecture of Lynch
Anurag K. Singh, Uli Walther
This concerns a conjecture of Lynch on annihilators of local cohomology modules; we present a counterexample that has dimension three.
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…
Étale cohomological dimension, a conjecture of Lyubeznik and bounds for arithmetic rank
Manoj Kummini, Uli Walther
We produce a criterion for open sets in projective -space over a separably closed field to have étale cohomological dimension bounded by . We use the criterion to exhibit…
Bockstein homomorphisms in local cohomology
Anurag K. Singh, Uli Walther
Let be a polynomial ring in finitely many variables over the integers, and fix an ideal of . We prove that for all but finitely prime integers , the Bockstein homomor…
Cohen-Macaulayness and computation of Newton graded toric rings
Mathias Schulze, Uli Walther
Let be a positive semigroup in generated by , and let be the associated semigroup ring over a field . We investigate heredity of the Cohen-Macaulay…
Local cohomology and pure morphisms
Anurag K. Singh, Uli Walther
We study a question raised by Eisenbud, Mustata, and Stillman regarding the injectivity of natural maps from Ext modules to local cohomology modules. We obtain some positive answer…
A connectedness result in positive characteristic
Anurag K. Singh, Uli Walther
Let be a complete local ring of positive dimension, which contains a separably closed coefficient field of prime characteristic. Using a vanishing theorem of Peskine-Szpiro…
On the arithmetic rank of certain Segre products
Anurag K. Singh, Uli Walther
We compute the arithmetic ranks of the defining ideals of homogeneous coordinate rings of certain Segre products arising from elliptic curves. The cohomological dimension of these…