6 papers · 1 filter
GL-algebras in positive characteristic III: the divided power algebra
Karthik Ganapathy
In this paper, we study GL-equivariant modules over the infinite-variable divided power algebra with an algebraically closed field of characteristi…
Derived equivalences via Tate resolutions
K. Ganapathy, Sarang Sane
For any finite sequence of elements in a commutative noetherian ring , we show that for , the natural map from the Koszul complex $K(s_1^n, \ldots ,…
GL-algebras in positive characteristic II: the polynomial ring
Karthik Ganapathy
We study GL-equivariant modules over the infinite variable polynomial ring with an infinite field of characteristic . We extend many of…
Ideal-theoretic non-noetherianity of polynomial functors in positive characteristic
Karthik Ganapathy
A long-standing open problem in representation stability is whether every finitely generated commutative algebra in the category of strict polynomial functors satisfies the noether…
Non-noetherian GL-algebras in characteristic two
Karthik Ganapathy
Over fields of characteristic two, we construct an infinite ascending chain of GL-stable ideals in the coordinate ring of infinite skew-symmetric matrices. This construction provid…
Resolutions of symmetric ideals via stratifications of derived categories
Karthik Ganapathy
We propose a method to unify various stability results about symmetric ideals in polynomial rings by stratifying related derived categories. We execute this idea for chains of $GL_…