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Session S07 - Differential operators in algebraic geometry and commutative algebra

Friday, July 16, 13:00 ~ 13:30 UTC-3

Primary decomposition with differential operators

Yairon Cid Ruiz

Ghent University , Belgium   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We introduce differential primary decompositions for ideals in a commutative ring. Ideal membership is characterized by differential conditions. The minimal number of conditions needed is the arithmetic multiplicity. Minimal differential primary decompositions are unique up to change of bases. Our results generalize the construction of Noetherian operators for primary ideals in the analytic theory of Ehrenpreis-Palamodov, and they offer a concise method for representing affine schemes. The case of modules is also addressed.

Joint work with Bernd Sturmfels (MPI-MiS Leipzig and UC Berkeley).

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