Constructing and transforming standard resolutions of local modules

TL;DR

This paper develops methods to construct and transform standard resolutions of local modules on complex hypersurfaces, linking algebraic techniques with categorical geometry and extending to complete intersections and arbitrary fields.

Contribution

It introduces a novel approach to standard resolutions using basis methods, with extensions to broader classes of varieties and algebraic settings.

Findings

Standard resolutions constructed for local modules on complex hypersurfaces.

Extensions of methods to complete intersections and arbitrary fields.

Applications to derived categories and categorical geometry.

Abstract

We construct standard resolutions for analytic local modules on complex hypersurfaces using standard basis methods, with extensions to complete intersections. The algebraic version over arbitrary infinite fields is also suggested. Applications include derived category formula of local hypersurface blow-ups, revealing new connections between standard bases and categorical geometry.