MSRI - Cohomological Approaches to Rational Points

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

To apply for funding, you must register by Mon, Jan 30 2006. Click to Register

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

Important

Additional Lodging information

Directions to MSRI

Schedule
Monday, March 27, 2006
9:30AM - 10:30AM	Minhyong Kim	Non-abelian Cohomology Varieties and Diophantine Geometry [Video available]
11:00AM - 12:00PM	Gaël Rémond	On a Conjecture of Pink [Video available]
2:15PM - 3:15PM	Shou-Wu Zhang	Distributions in Arithmetic Dynamics [Video available]
3:45PM - 4:45PM	Carlo Gasbarri	Dyson’s Theorem for the Product of Two Curves [Video available]
Tuesday, March 28, 2006
9:30AM - 10:30AM	Helene Esnault	Rational Points over Finite Fields and Cohomological Methods [Video available]
11:00AM - 12:00PM	János Kollár	A Conjecture of Ax and Degenerations of Fano Varieties [Video available]
2:15PM - 3:15PM	Jason Starr	Rational 1-connectedness and Rational Points [Video available]
3:45PM - 4:45PM	Max Lieblich	Period and Index in the Brauer Group of a Relative Curve [Video available]
Wednesday, March 29, 2006
9:30AM - 10:30AM	Shuji Saito	Weak Bloch-Beilinson Conjecture for Zero Cycles over p-adic Fields. (joint work with Kanetomo [Video available]
11:00AM - 12:00PM	Alexander Merkurjev	Zero-cycles on Homogeneous Varieties [Video available]
2:15PM - 3:15PM	Emmanuel Peyre	Height Zeta Functions : An Arithmetic-motivic Dictionary [Video available]
3:45PM - 4:45PM	David Bourqui	Height Zeta Functions : The Case of Toric Varieties [Video available]
Thursday, March 30, 2006
9:30AM - 10:30AM	Michael Stoll	Finite Descent Obstructions and Rational Points [Video available]
2:15PM - 3:15PM	Philippe Gille	Rational Points on Homogeneous Spaces : A Survey [Video available]
3:45PM - 4:45PM	David Harari	1-Motives and Principal Homogeneous Spaces of Algebraic Groups [Video available]
Friday, March 31, 2006
9:30AM - 10:30AM	Alexei Skorobogatov	The Elementary Obstruction for Homogeneous Spaces [Video available]
11:00AM - 12:00PM	Karl Rubin	Growth of Ranks of Abelian Varieties in Dihedral Extensions [Video available]

Parent Program(s):
Rational and Integral Points on Higher-Dimensional Varieties

Questions about this workshop should be sent either by email to 302@msri.org
or by regular mail to:

Cohomological Approaches to Rational Points Mathematical Sciences Research Institute 17 Gauss Way, Berkeley, CA 94720-5070. USA

The Institute is committed to the principles of Equal Opportunity and Affirmative Action.