11:00

### On fields with the absolute Galois group of Q

## Abstract

.. showing that a field K is isomorphic to Q if it has the same absolute Galois group and if it satisfies a very small additional condition (very similar to my talk 2 years ago).

Forthcoming events in this series

Thu, 04 May 2017

11:00

11:00

C5

Jochen Koenigsmann

(Oxford)

.. showing that a field K is isomorphic to Q if it has the same absolute Galois group and if it satisfies a very small additional condition (very similar to my talk 2 years ago).

Tue, 07 Mar 2017

11:00

11:00

C5

Laura Capuano

(Oxford)

What makes an intersection likely or unlikely? A simple dimension count shows that two varieties of dimension r and s are non "likely" to intersect if r < codim s, unless there are some special geometrical relations among them. A series of conjectures due to Bombieri-Masser-Zannier, Zilber and Pink rely on this philosophy. I will speak about a joint work with F. Barroero (Basel) in this framework in the special case of a curve in a family of elliptic curves. The proof is based on Pila-Zannier method, combining diophantine ingredients with a refinement of a theorem of Pila and Wilkie about counting rational points in sets definable in o-minimal structures.

Everyone welcome!

Thu, 23 Feb 2017

11:00

11:00

C5

Alfonso Ruiz

(Oxford)

Using results by Eisenbud, Schoutens and Zilber I will propose a model theoretic structure that aims to capture the algebra (or geometry) of a non reduced scheme over an algebraically closed field.

Thu, 02 Feb 2017

11:00

11:00

C4

Nicholas Wentzlaff-Eggebert

(Oxford)

Abstract: We will consider a model theoretic approach to Gelfand-Naimark duality, from the point of view of (generalized) Zariski structures. In particular we will show quantifier elimination for compact Hausdorff spaces in the natural Zariski language. Moreover we may see a slightly unusual construction and tweak to the language, which improves stability properties of the structures.

Thu, 19 Jan 2017

11:00

11:00

C5

Ugur Efem

In this talk I will present some answers to the question when every specialisation from a \kappa-saturated extension of

a Zariski structure is \kappa-universal? I will show that for algebraically closed fields, all specialisations from a \kappa-

saturated extension is \kappa-universal. More importantly, I will consider this question for finite and infinite covers of

Zariski structures. In these cases I will present a counterexample to show that there are covers of Zariski structures

which have specialisations from a \kappa-saturated extension that are not \kappa-universal. I will present some natural

conditions on the fibres under which all specialisations from a \kappa-saturated extension of a cover is \kappa-universal.

I will explain how this work points towards a prospective Ladder Theorem for Specialisations and explain difficulties and

further works that needs to be considered.

Thu, 01 Dec 2016

11:00

11:00

C5

Thu, 24 Nov 2016

11:00

11:00

C5

Thu, 16 Jun 2016

11:00 -
15:45

C3

Andres Villaveces

(Bogota)

Abstract: finding a "non-commutative limit" of the j-invariant (to real numbers, in a way that captures reasonably well the connection with extensions of number fields) has prompted several approaches (Manin-Marcolli, Castaño-Gendron). I will describe one of these approaches in a brief way, and I will make some connections to the model theory of sheaves.

Thu, 02 Jun 2016

11:00

11:00

C5

Thu, 19 May 2016

11:00

11:00

C5

Vahagn Aslanyan

(Oxford)

Thu, 28 Apr 2016

11:00

11:00

C5

Jochen Koenigsmann

(Oxford)

This will be a little potpourri containing some of the recent developments on the model theory of F_p((t)) and of algebraic extensions of Q_p.

Thu, 25 Feb 2016

11:00

11:00

C5

Thu, 11 Feb 2016

11:00

11:00

C5

Thu, 04 Feb 2016

11:00

11:00

C5

Vahagn Aslanyan

(Oxford)

Thu, 28 Jan 2016

11:00

11:00

C5

Philip Dittmann

(Oxford)

"We give a diophantine criterion for a polynomial with rational coefficients not to have any

rational zero, i.e. an existential formula in terms of the coefficients expressing this property. This can be seen as a kind of restricted

model-completeness for Q and answers a question of Koenigsmann."

Thu, 21 Jan 2016

11:00

11:00

C5

Thu, 03 Dec 2015

11:00

11:00

C5

B Zilber

(Oxford)

following the joint paper with L.Shaheen http://people.maths.ox.ac.uk/zilber/wLb.pdf

Thu, 05 Nov 2015

11:00

11:00

C5

Thu, 22 Oct 2015

11:00

11:00

C5

Alfonso Guido Ruiz

(Oxford)

I will explain how algebraic spaces can be presented as Zariski geometries and prove some classical facts about algebraic spaces using the theory of Zariski geometries.

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