Ganapathy Krishnamoorthy

arXiv2026

Derived equivalences for chain complexes with support

For a Serre subcategory $\mathscr L$ and a resolving subcategory $\mathscr A$ of an abelian category, we show that the derived equivalence $D^b(\overline{\mathscr A} \cap \mathscr L) \simeq D^b_{\mathscr L}(\mathscr A)$ holds under certain conditions. We apply this to obtain derived equivalences in the contexts of chain complexes of graded modules or coherent sheaves, with finite $\mathscr A$-dimension, supported on closed sets having eventually finite $\mathscr A$-dimension. Using this, we obtain descriptions of the homotopy fibers in (hermitian) K theory of the restriction maps to certain open sets.

math.CT↗

arXiv2025

Extremal behavior of ideals of minors

Let $(R,\mathfrak m,\mathsf k)$ be either a fiber product or an artinian stretched Gorenstein ring, with $\operatorname{ch}(\mathsf k)\neq 2$ in the latter case. We prove that the ideals of minors of the minimal free resolution of any finitely generated $R$-module are eventually 2-periodic. Moreover, if the embedding dimension of $R$ is at least 3, eventually the ideals of minors become the powers of the maximal ideal, yielding the 1-periodicity. These are analogs of results obtained over complete intersections and Golod rings by Brown, Dao, and Sridhar. We also study the transfer of periodicity between rings. Specifically, we prove that for any local ring $(R,\mathfrak m)$, if $x\in \mathfrak m$ is a super-regular element and $M$ is an $R/(x)$ module whose ideals of minors are asymptotically the powers of the maximal ideal over $R/(x)$, then the same holds for the ideals of minors of $M$ over $R$.

math.AC↗