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arXiv · 1807.05471

The Cohomology Annihilator of a Curve Singularity

Özgür Esentepe
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Abstract

The aim of this paper is to study the theory of cohomology annihilators over commutative Gorenstein rings. We adopt a triangulated category point of view and study the annihilation of stable category of maximal Cohen-Macaulay modules. We prove that in dimension one the cohomology annihilator ideal and the conductor ideal coincide under mild assumptions. We present a condition on a ring homomorphism between Gorenstein rings which allows us to carry the cohomology annihilator of the domain to that of the codomain. As an application, we generalize the Milnor-Jung formula for algebraic curves to their double branched covers. We also show that the cohomology annihilator of a Gorenstein local ring is contained in the cohomology annihilator of its Henselization and in dimension one the cohomology annihilator of its completion. Finally, we investigate a relation between the cohomology annihilator of a Gorenstein ring and stable annihilators of its noncommutative resolutions.

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Özgür Esentepe. 2021-07-21. The Cohomology Annihilator of a Curve Singularity. https://doi.org/10.1016/j.jalgebra.2019.08.037

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