Videolibrary
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
Video Library
Archive
Most viewed videos

Search
RSS
New in collection






International conference "Birational and affine geometry"
April 27, 2012 11:00–11:50, Moscow, Steklov Mathematical Institute of RAS
 


Remarks on self-maps with fixed points over a number field

E. Yu. Amerik

National Research University "Higher School of Economics"
Video records:
Flash Video 367.7 Mb
Flash Video 2,235.8 Mb
MP4 1,397.0 Mb

Number of views:
This page:862
Video files:311

E. Yu. Amerik
Photo Gallery



Abstract: Let $f\colon X\dashrightarrow X$ be a rational self-map with a fixed point $q$, where everything is defined over a number field $K$. We make some remarks on the dynamics of $f$ in a $p$-adic neighbourhood of $q$ for a suitable prime $p$. In particular we show that if the eigenvalues of $Df_q$ are multiplicatively independent, then “most” algebraic points on $X$ have Zariski-dense iterated orbits. (The starting motivation for this was an effort to find an easier proof of the potential density of the variety of lines on a cubic fourfold, due to Voisin and myself. If time permits, I shall also sketch this easier proof.) The talk is based on joint work with Bogomolov and Rovinsky.

Language: English
 
  Contact us:
 Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024