2024/06/06 by Hancharuk, Aliaksandr, Laurent-Gengoux, Camille, Strobl, Thomas · 1 citation
#13A15 #13D02 #14F08 #55P43 #Algebraic Topology (math.AT) #Commutative Algebra (math.AC) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2406.03955
Given a commutative algebra \mathcal O, a proper ideal \mathcal I, and a resolution of \mathcal O/ \mathcal I by projective \mathcal O -modules, we construct an explicit Koszul-Tate resolution. We call it the arborescent Koszul-Tate resolution since it is indexed by decorated trees. When the \mathcal O-module resolution has finite length, only finitely many operations are needed in our constructions -- this is to be compared with the classical Tate algorithm, which requires infinitely many such computations if \mathcal I is not a complete intersection. As a by-product of our construction, the initial projective \mathcal O -module resolution becomes equipped with an explicit A_∞-algebra.