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Workshop

Cohomological Approaches to Rational Points March 27, 2006 - March 31, 2006
Registration Deadline: February 25, 2006 over 8 years ago
To apply for Funding you must register by: December 27, 2005 almost 9 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
Speaker(s)

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Description

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.

Funding & Logistics Show All Collapse

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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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MSRI has preferred rates at the Rose Garden Inn, depending on room availability. 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 the MSRI rate on all room types available.

MSRI has preferred rates 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 123MSRI. Our preferred rate is $139 per night for a Deluxe Queen/King, based on availability.

MSRI has preferred rates of $149 - $189 plus tax at the Hotel Shattuck Plaza, depending on room availability. Guests can either call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Inst. discount; or go to www.hotelshattuckplaza.com and click Book Now. Once on the reservation page, click “Promo/Corporate Code“ and input the code: msri.

MSRI has preferred rates of $110 - $140 at the Berkeley Lab Guest House, depending on room availability. Reservations may be made by calling 510-495-8000 or directly on their website. Select “I am an individual traveler affiliated with MSRI”.

Additional lodging options may be found on our short term housing page.

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Schedule
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Mar 27, 2006
Monday
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
Tuesday
09:30 AM - 10:30 AM
  Rational Points over Finite Fields and Cohomological Methods
Hélène Esnault (FU 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
Wednesday
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
Thursday
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
Friday
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)