NoGAGS Berlin 2012

Freie Universität Berlin December 06-07, 2012 - A joint seminar with Bremen, Humboldt University Berlin, FU Berlin, Groningen, Hamburg, and Hannover. (Other NoGAGS meetings can be found [here])

Organizers

Alexander Schmitt, Anna Wißdorf

Schedule

Time	Thursday, 06.12.	Friday, 07.12.
9:30		T. Finis (FU Berlin) "An approximation theorem for congruence subgroups"
10:30		Coffee
11:00		J. Kass (Hannover) "What is H_{1}(Abel map)? "
12:00	Lunch	Lunch
14:00	S. Rollenske (Bielefeld)	P. Sosna (Hamburg) "On the Jordan-Hölder property for geometric derived categories "
15:00	Coffee	Coffee
15:30	F. Gounelas (HU Berlin) "Free curves on varieties"	tba
16:30	Coffee	Coffee
17:00	A. Anema (Groningen) "Covering spaces of an elliptic curve that ramify only above one point"
18:30	Dinner at Eierschale

Abstracts

• A. Anema: "Covering spaces of an elliptic curve that ramify only above one point"

ABSTRACT: This talk deals with finite maps to elliptic curves E defined over the complex numbers. From algebraic topology and the theory of Riemann surfaces, one knows there exist curves D admitting a finite map g : D --> E such that g ramifies only above one point of E. We consider the problem of explicitly constructing such pairs (D, g). This is done by looking at torsion of the elliptic surface corresponding to y^2=x^3+ax+b over the curve E given by 4a^3+27b^2=1.

• T. Finis: "An approximation theorem for congruence subgroups"

ABSTRACT: By a classic theorem of Jordan (1878), every finite subgroup of GL (n, K), where K is a field of characteristic zero, contains an abelian normal subgroup of index at most J(n), where J(n) depends only on n. In characteristic p the situation is of course different. A theorem of Nori (1987) says that for all n > 0 and all primes p with p > N(n), where N is a suitable function, the subgroups of GL (n, F_p) which are generated by their elements of order p are described by connected algebraic subgroups of GL (n) defined over F_p. This result can be combined with Jordan's theorem to describe arbitrary subgroups (cf. also Larsen-Pink 2011).

Let G be a reductive algebraic group defined over Q. In the talk I will present an approximation theorem for subgroups of G (Z/p^N Z) (or, equivalently, for open subgroups of G (Z_p)), which provides a partial description of these subgroups in terms of connected algebraic subgroups of G defined over Q_p. The theorem has applications to the theory of congruence subgroups of arithmetic groups, in particular to the limit multiplicity problem. The results are joint work with Erez Lapid (Jerusalem/Rehovot).

• F. Gounelas: "Free curves on varieties"

ABSTRACT: We study various ways in which a variety can be "connected by curves of a fixed genus", mimicking the notion of rational connectedness. At least in characteristic zero, in the specific case of the existence of a single curve with a large unobstructed deformation space of morphisms to a variety implies that the variety is in fact rationally connected. Time permitting I will discuss attempts to show this result in positive characteristic.

• J. Kass: "What is H_{1}(Abel map)? "

ABSTRACT: A smooth curve over the complex numbers admits an Abel map, that is, an embedding into the complex torus known as the Jacobian, and the homomorphism on homology induced by the Abel map can be identified with the Poincaré Duality isomorphism. I will describe how this result extends to singular curves. In doing so, I will describe the compactified Jacobian of a curve with axis-like singularities, a result that is of independent interest.

• P. Sosna: "On the Jordan-Hölder property for geometric derived categories"

ABSTRACT: We prove that the semiorthogonal decompositions of the derived category of the classical Godeaux surface X do not satisfy the Jordan-Hölder property. More precisely, we will show that there are two maximal exceptional sequences in this category, one of length 11, the other of length 9. This is joint work with C. Böhning und H.-C. Graf von Bothmer.

Registration

To register, please send an email mentioning your name, affiliation and whether you want to attend the conference dinner to Mrs Metzler.

Hotels

There is a limited capacity at Seminaris CampusHotel and Best Western Steglitz. Please make your own reservation. Details will be send to you with registration.

Other possibilities include Hotel Am Wilden Eber and Metropolitan Berlin.

Travel Information

How to get to the institute.

Participants

• A. Apostolov (Hannover)
• Chiara Camere (Hannover)
• Wolfgang Ebeling (Hannover)
• Andreas Hochenegger (Köln)
• Klaus Hulek (Hannover)
• Michael Lönne (Hannover)
• Stefano Pascolutti (Hannover)
• David Ploog (Hannover)
• Sönke Rollenske (Bielefeld )
• Matteo Tommasini (Hannover)