Philip Dittmann (Oxford): First-order logic in finitely generated fields
Thursday, 10.01.2019 11:00 im Raum SR 1D
The expressive power of first-order logic in the class of finitely
generated fields, as structures in the language of rings, is relatively
poorly understood. For instance, Pop asked in 2002 whether elementarily equivalent finitely generated fields are necessarily isomorphic, and this is still not known in the general case.
Building on work of Pop and Poonen, and using cohomological techniques based on tools due to Kerz-Saito and Gabber, I shall show that every infinite finitely generated field of characteristic not two admits a definable subring which is a finitely generated algebra over a global field. This implies that any such finitely generated field is biinterpretable with arithmetic, and gives a positive answer to the question above in characteristic not two.
Angelegt am Monday, 07.01.2019 09:35 von Martina Pfeifer
Geändert am Monday, 07.01.2019 09:35 von Martina Pfeifer
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