Some model theory of fields with commuting operators
Speaker(s): Jan Dobrowolski(Xiamen University Malaysia)
Time: 16:00-17:00 March 27, 2025
Venue: Room 9, Quan Zhai, BICMR
Abstract:
After a brief introduction, I will present some details of the proof of the result we have obtained with O. Leon Sanchez, which says that if D is a local algebra, then the theory of fields with D-operators satisfying a general compatibility condition is always companionable in characteristic zero, and is companionable in positive characteristic if the maximal ideal of D coincides with the kernel of the Frobenius homomorphism on D.
Examples falling into this framework include the theory of fields with commuting D-operators, the theory of fields with Lie-commuting derivations, the theory of fields with iterative Hasse-Schmidt derivations, and, more generally, the theory of fields with finite group scheme actions.
Hybrid: Both in-person and online
Quan 9 & zoom room: 717 463 6082