# Mathematical Sciences Research Institute

Home » Cohomological Approaches to Rational Points

# Workshop

Cohomological Approaches to Rational Points March 27, 2006 - March 31, 2006
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

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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.

## Show Lodging

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 MSRI123. Our preferred rate is $129 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
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)