Oberseminar Logik - SoSe 2024
Organizers
- Prof. Dr. Philipp Hieronymi
- Dr. Tingxiang Zou
Time and location
Unless stated otherwise: Mondays 17.00-18.00 in SemR N0.003, Endenicher Allee 60.
The participants of the seminar are welcome for coffee and tea in room 4.005 (office Hieronymi) at 16.30 before the talks.
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Talks
- April 8th: No seminar
- April 15th: No seminar
- April 22nd: Martin Hils (Münster)
Title: Model theory of valued fields with non-standard Frobenius automorphism
Abstract: In the talk, we will give an overview of the model theory of the limit - where p tends to infinity - of the Frobenius automorphism acting on an algebraically closed non-trivially valued field of characteristic p,
and similarly in the Witt-Frobenius case. We will in particular discuss
i) the classification of imaginaries by the geometric sorts (from a recent joint work with Rideau-Kikuchi);
ii) model-theoretic tameness results (obtained in joint work with Chernikov), and
iii) an application to pseudofinite difference fields concerning estimates on the number of rational points (obtained in joint work with Hrushovski, Zou and Ye). - April 29th: Simone Ramello (Münster)
Title: Model theory of endomorphisms of valued fields
Abstract: We tackle the problem of understanding theories of valued fields endowed with a possibly non-surjective endomorphism,
the most prominent example being the limit of the action of Frobenius on non-trivially valued separably closed valued fields of positive characteristic.
We establish an embedding theorem for such valued difference fields, building on previous work of Pal (in the inversive case) and Dor-Halevi (in the contracting case),
and deduce Ax-Kochen/Ershov-style principles. - May 6th: Konstantinos Kartas (IMJ-PRG/Sorbonne)
Title: On Ci fields
Abstract: Given a natural number i, a field k is called Ci if every homogeneous polynomial over k of degree d in more than d^i variables has a non-trivial zero.
Emil Artin had famously conjectured that Qp is C2. While this was refuted by Terjanian, an appropriate asymptotic version for p where p tends to infinity was proved by Ax-Kochen.
In a somewhat orthogonal direction, we fix p but instead let the ramification go to infinity. We show that any maximal totally ramified extension of Qp is C1.
The two main ingredients are Esnault’s result on degenerations of rationally connected varieties over finite fields and F.-V. Kuhlmann’s theory of tame fields. - May 13th: Nigel Pynn-Coates (Vienna)
- May 20th: No seminar
- May 27th: Adrian De Lon (Bonn)
- June 3rd: No seminar
- June 10th: No seminar
- June 17th: Pablo Suárez-Serrato (UNAM/MPIM)
- June 24th: TBA
- July 1st: TBA
- July 8th: TBA
- July 15th: TBA