Seminario di Geometria Aritmetica, Motivi e Teoria dei numeri
Working group on p-adic families
This year seminar is devoted to understanding the recent works of G. Stevens and E. Urban on the construction of eigenvarieties associated to reductive groups over Q and of E. Urban and C. Skinner on the main conjecture for elliptic curves.
The first part of the seminar is a review of Stevens' theory of p-adic cohomological families for GL_2 via modular symbols. In the second part, January-March 2011, we will study the paper by Ash and Stevens where Stevens' approach is generalized to other reductive groups. Eventually, in April-June 2011 we will discuss the works of Urban and Skinner-Urban.
October 29, 14.00-16.00, Aula Dottorato, Fabrizio Andreatta Introduction. Stevens' approach to p-adic families via modular symbols
November 26 ( date change! ), 14.00-16.00, Aula C, Rodolfo Venerucci The Eichler-Shimura isomorphism. Hida families following Greenberg-Stevens.
December 3, 14.00-16.00, Aula C, Marco Seveso Slope decompositions according to Ash-Stevens.
December 22, 14.00-16.00, Aula C, Riccardo Brasca Comparison theorem and Control theorem for GL_2.
February 18, 10.30-12.30, Aula C, Marco Seveso Introduction to theory of buldings following Bruhat-Tits I.
February 25, 14.00-16.00, Aula C, Marco Seveso Introduction to theory of buldings following Bruhat-Tits II.
Next metting is planned for March 25th.
A series of Lectures on "Motives & Weights" by Prof.
M. Bondarko, September-November 2010
A series of lectures
will be given by Prof. M. Bondarko (St. Petersburg State
University) visiting our Department from September 27 to November
27 under the framework of a Cariplo Foundation Fellowship settled
by the Landau Network-Centro Volta
http://www.centrovolta.it/landau/
Abstract: Weight
structures for triangulated categories are natural counterparts of
t-structures. They were originally introduced in order to define
(certain) weights for Voevodsky's motives. These motives are very
important for algebraic geometry, and will be one of the main
subjects of the lectures. Besides, there are a lot of examples
when non-canonical constructions yield important functorial
information: projective and injective resolution of objects and
complexes over abelian categories allow to define derived
functors; nice compactifications and smooth hyper-resolutions of
varieties yield weight spectral sequences for etale and singular
cohomology; skeletal filtration for topological spectra allow to
construct Atiyah-Hirzebruch spectral sequences for their
cohomology. All of these observations have very natural
'explanations' inside the theory of weight structures! All of
these matters will also be mentioned in the lectures.
The lectures will take place in Aula Dottorato of the
Math Department "F. Enriques" from 3 (sharp) to 5 p.m. (2 academic
hour lectures) as follows:
I. Thursday October 21, II. Thursday
October 28, III. Thursday November 4, IV. Monday November 8, V. Thursday November 11, VI.
Thursday November 18, VII. Monday November 22, VIII. Thursday November 25
Seminario di Geometria
Aritmetica, Motivi e Teoria dei Numeri
2009/2010