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 9 years ago
To apply for Funding you must register by: December 27, 2005 almost 10 years ago
Parent Program: Rational and Integral Points on Higher-Dimensional Varieties
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.

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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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A block of rooms has been reserved at the Rose Garden Inn. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show MSRI rate on all room types available.

A block of rooms has been reserved at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123. Our preferred rate is $129 per night for a Deluxe Queen/King, based on availability.

Additional lodging options (short term housing page - Short Term Housing

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Mar 27, 2006
09:30 AM - 10:30 AM
  Non-abelian Cohomology Varieties and Diophantine Geometry
Minhyong Kim
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
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
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)