CRM: Centro De Giorgi
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ERC Research Period on Diophantine Geometry

Algebraic dynamics, difference fields and model theory (30')

speaker: Zoé Chatzidakis (Institut de Mathématiques de Jussieu, Université Paris 7)

abstract: (Joint work with E. Hrushovski). M. Baker proved in 2007 that given a endomorphism f of P1 of degree >1 and defined over a function field K, either all points of P1(K) of canonical height 0 are preperiodic, or the endomorphism f descends to the field of constants of K. Szpiro and Tucker asked about generalising the result to higher dimensional varieties. A reformulation by Szpiro of the hypotheses in terms of limited sets allowed model theory to get into the picture, more precisely the model theory of difference fields. We were therefore able to give the correct formulation of the descent result in higher dimension, and prove it.

In the talk I will state our results, and explain the concepts involved.


timetable:
Tue 2 Oct, 10:30 - 11:00, Sala Conferenze Centro De Giorgi
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