Research Papers

Derivations of Artinian complete intersections

A. G. Aleksandrov

V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences

Abstract: The paper is devoted to the study of derivations of local Artinian algebras which are complete intersections. The main result is a proof of a long-standing conjecture which asserts that there are no derivations of negative weights on positively graded Artinian complete intersections. A key role in the proof is played by the following little-known fact: the canonical primary decomposition of an invariant ideal under derivations is also invariant.

Keywords: Artinian algebras, derivations, zero-dimensional singularities, complete intersections, vector fields, canonically primary decomposition, invariance, deformations.

Received: 09.06.2025