Wintersemester 2009/2010 - Research Seminar: The Eigencurve

• Date: Thursday, 10-12 a.m.
• Place: T03 R04 D10
• Starting date: 15 October 2009
• The language of the seminar will be English.
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Description

The main topics of this seminar are p-adic modular forms and the eigencurve.

Organisers

Ulrich Görtz, Gebhard Böckle and Gabor Wiese

Programme

Latest version of the programme.

List of Lectures

	Date	Speaker	Title
1	15/10/2009	Gebhard Böckle	Overview and motivation
2	22/10/2009	Philipp Hartwig	Rigid analytic geometry I
3	29/10/2009	Eduardo Ocampo	Rigid analytic geometry II
4	05/11/2009	Tommaso Centeleghe	Modular forms à la Katz
5	12/11/2009	Panos Tsaknias	The Eisenstein family
6	19/11/2009	Ralf Butenuth	p-adic modular forms à la Coleman
7	26/11/2009	Martin Kreidl	p-adic Banach spaces
8	03/12/2009	Archie Karumbidza	The Atkin-Lehner operator U_p and the Hecke algebra I
9	10/12/2009	Oliver Bültel	The Atkin-Lehner operator U_p and the Hecke algebra II
10	17/12/2010	Stefan Kukulies	Fredholm theory
11	07/01/2010	Haluk Sengün	Pseudo-representations I
12	14/01/2010	Juan Cerviño	Pseudo-representations II
13	21/01/2010	Johan Bosman	The eigencurve
14	28/01/2010	Gabor Wiese	Properties of the eigencurve
15	04/02/2010	--	(no talk)

References

• Berthelot, P., Cohomologie rigide et cohomologie rigide à support propre, Premère partie, Prépublication IRMAR 96-03, 89 pages (1996).
• S. Bosch, Lectures on Formal and Rigid Geometry, SFB 478-Preprint 378, Münster.
• S. Bosch, U. Güntzer, R. Remmert, Non-archimedian analysis, Springer Grundlehren 261, Springer 1984.
• K. Buzzard, Families of modular forms, J. Th. Nombres de Bordeaux 13 (2001), 43--52.
• K. Buzzard, Eigenvarieties in: L-functions and Galois representations, London Math. Soc. Lecture Note Ser. 320, Cambridge Univ. Press 2007, 59--120.
• K. Buzzard, Eigenvarieties, (hand-written) lecture notes of a course at Harvard University.
• R. Coleman, Classical and overconvergent modular forms, Invent. math. 124 (1996), 215--241.
• R. Coleman, Banach spaces and families of modular forms, Invent. math. 127 (1997), 417--479.
• R. Coleman, B. Mazur, The eigencurve, in: Galois representations in arithmetic algebraic geometry, eds. A. Scholl, R. Taylor (Durham 1996). London Math. Soc. Lecture Note Ser. 254, Cambridge Univ.~Press 1998, 1--113.
• M. Emerton, On the interpolation of systems of eigenvalues attached to automorphic Hecke eigenforms, Invent. math. 164, no. 1 (2006), 1--84.
• J. Fresnel, M. van der Put, Géométrie analytique rigide et applications, Birkhäuser 1981.
• F. Gouvêa, Arithmetic of p-adic modular forms, Springer Lecture Notes in Math. 1304 (1988).
• P. Kassaei, The eigencurve: a brief survey, in: Math. Inst. Göttingen Seminars, ed. Y. Tschinkel, Göttingen 2005.
• N. Katz, p-adic properties of modular schemes and modular forms, in: Modular Functions of One Variable III, Springer Lecture Notes in Math. 350 (1972), 69--190.
• P. Schneider, Basic notions of rigid analytic geometry, Galois representations in arithmetic algebraic geometry (Durham, 1996), 369?378, London Math. Soc. Lecture Note Ser., 254, Cambridge Univ. Press, Cambridge, 1998.
• J.-P. Serre, Endomorphismes complètement continues des espaces de Banach p-adiques, Publ. Math. IHES 12 (1962), 69--85.

Last modification: 27 January 2010.