Session S07 - Differential operators in algebraic geometry and commutative algebra

Friday, July 16, 14:00 ~ 14:30 UTC-3

Differential powers in mixed characteristic

Eloísa Grifo

University of Nebraska – Lincoln, United States of America   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The differential operators version of the Zariski--Nagata theorem says that over a polynomial ring over a perfect field, the differential powers of a radical ideal coincide with its symbolic powers. In mixed characteristic, differential powers are larger than symbolic powers, but there is a version of Zariski--Nagata that works when we mix in p-derivations.

In singular rings, differential powers can still be used as tools to prove results about symbolic powers, even though the two notions no longer coincide. We will discuss a uniform Chevalley theorem for direct summands of polynomial rings in mixed characteristic by introducing a new type of differential powers, which do not require the existence of a p-derivation on the direct summand.

Joint work with Alessandro De Stefani (University of Genova, Italy) and Jack Jeffries (University of Nebraska--Lincoln, United States of America).

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