K. Ganapathy

collaborators

5 papers

math.AC2026

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 $D = Div (k^{\infty})$ with $k$ an algebraically closed field of characteristi…

math.AC2026

Derived equivalences via Tate resolutions

K. Ganapathy, Sarang Sane

For any finite sequence of elements $s_{1}, \dots, s_{d}$ in a commutative noetherian ring $R$ , we show that for $n ≫ 0$ , the natural map from the Koszul complex $K(s_1^n, \ldots ,…

math.RA2025

Noncommutative invariants of finite and classical groups

Karthik Ganapathy

We investigate the structure of the invariant subring of the tensor algebra $T (W)$ of a $G$ -representation $W$ , viewed as a twisted commutative algebra (tca). For a faithful repres…

math.AC2025

GL-algebras in positive characteristic II: the polynomial ring

Karthik Ganapathy

We study GL-equivariant modules over the infinite variable polynomial ring $S = k [x_{1}, x_{2}, ..., x_{n}, ...]$ with $k$ an infinite field of characteristic $p > 0$ . We extend many of…

math.AC2025

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…