Mathematical Sciences Research Institute

Home » Cohomological Approaches to Rational Points


Cohomological Approaches to Rational Points March 27, 2006 - March 31, 2006
Registration Deadline: February 25, 2006 over 17 years ago
To apply for Funding you must register by: December 27, 2005 over 17 years ago
Parent Program:
Organizers Fedor Bogomolov, Antoine Chambert-Loir, Jean-Louis Colliot-Thélène (chair), A. Johan de Jong, Raman Parimala

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This workshop will explore the various ways in which cohomology gives information on the existence and density of rational points. Here are the main topics to be covered. Étale cohomology of varieties over number fields: the Brauer-Manin obstruction and beyond. Étale cohomology of varieties over finite fields: as an example, Esnault's result that smooth rationally connected varieties over a finite field have a rational point. Coherent cohomology, deformation methods: applications to varieties over function fields in one or two variables over the complex field, also to varieties over finite and local fields. Arakelov geometry, algebraic geometry over the algebraic closure of the rationals, connexions with hyperbolicity, distribution of algebraic points of small height.
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification
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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

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Schedule, Notes/Handouts & Videos
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Mar 27, 2006
09:30 AM - 10:30 AM
  Non-abelian Cohomology Varieties and Diophantine Geometry
Minhyong Kim (International Centre for Mathematical Sciences)
11:00 AM - 12:00 PM
  On a Conjecture of Pink
Gaël Rémond
02:15 PM - 03:15 PM
  Distributions in Arithmetic Dynamics
Shou-Wu Zhang (Princeton University)
03:45 PM - 04:45 PM
  Dyson’s Theorem for the Product of Two Curves
Carlo Gasbarri
Mar 28, 2006
09:30 AM - 10:30 AM
  Rational Points over Finite Fields and Cohomological Methods
Hélène Esnault (Freie Universität Berlin)
11:00 AM - 12:00 PM
  A Conjecture of Ax and Degenerations of Fano Varieties
János Kollár (Princeton University)
02:15 PM - 03:15 PM
  Rational 1-connectedness and Rational Points
Jason Starr
03:45 PM - 04:45 PM
  Period and Index in the Brauer Group of a Relative Curve
Max Lieblich (University of Washington)
Mar 29, 2006
09:30 AM - 10:30 AM
  Weak Bloch-Beilinson Conjecture for Zero Cycles over p-adic Fields. (joint work with Kanetomo
Shuji Saito
11:00 AM - 12:00 PM
  Zero-cycles on Homogeneous Varieties
Alexander Merkurjev
02:15 PM - 03:15 PM
  Height Zeta Functions : An Arithmetic-motivic Dictionary
Emmanuel Peyre
03:45 PM - 04:45 PM
  Height Zeta Functions : The Case of Toric Varieties
David Bourqui
Mar 30, 2006
09:30 AM - 10:30 AM
  Finite Descent Obstructions and Rational Points
Michael Stoll (Universität Bayreuth)
02:15 PM - 03:15 PM
  Rational Points on Homogeneous Spaces : A Survey
Philippe Gille
03:45 PM - 04:45 PM
  1-Motives and Principal Homogeneous Spaces of Algebraic Groups
David Harari
Mar 31, 2006
09:30 AM - 10:30 AM
  The Elementary Obstruction for Homogeneous Spaces
Alexei Skorobogatov
11:00 AM - 12:00 PM
  Growth of Ranks of Abelian Varieties in Dihedral Extensions
Karl Rubin (University of California, Irvine)