Oberseminar Zahlentheorie (WS 2012/13)
Winter 2012/13, Wednesdays, 16:30, room B 251 (Mathematisches Institut, Theresienstr. 39, 80333 München)
|Tuesday, 23.10.12, B252||Christian Okonek (Universität Zürich)||Intrinsic signs and lower bounds in real algebraic geometry|
|7.11.12||Andreas Rosenschon (LMU München)||On SK1 of curves I|
|14.11.12||Andreas Rosenschon (LMU München)||On SK1 of curves II|
|21.11.12||Dmitriy Izychev (Universität Heidelberg)||Equivariant ε-conjecture for unramified twists of Zp(1)|
|28.11.12||Anna Böttcher (UniBw München)||Harmonische Koketten auf dem Bruhat-Tits-Gebäude der GLn|
|19.12.12||Fabian Gundlach (LMU)||Sums of two squares and a power|
|9.1.13||Lenny Taelman (Universiteit Leiden)||Arithmetic of Drinfeld modules|
|6.2.13||Takashi Miura (UniBw München)||On the Fitting ideals of ideal class groups of non-cyclic CM-extensions|
|13.2.13||Wojtek Gajda (Uniwersytet im. Adama Mickiewicza)||Abelian varieties and l-adic representations||in der 1. Woche der vorlesungsfreien Zeit|
Lenny Taelman (Universiteit Leiden): Arithmetic of Drinfeld modules (9.1.13)
Drinfeld modules are function field objects that are analogs of elliptic curves (or of the multiplicative group) over number fields. They were introduced by Drinfeld in the 1970s, although parts of the theory had been discovered already in the 1930s by Carlitz. In this talk I will survey the more arithmetic aspects of Drinfeld modules, focussing on some recent finiteness theorems analogous to the Mordell-Weil theorem (or Dirichlet's unit theorem) and the finiteness of Sha (or of the class group), and on special values of L-functions. I will not assume any prior knowledge of Drinfeld modules.
Wojtek Gajda (Uniwersytet im. Adama Mickiewicza): Abelian varieties and l-adic representations (13.2.13)
We will discuss some recent computations of monodromies for abelian varieties over finitely generated fileds of arbitrary characteristics. In the second part of the talk I plan to explain independence (in the sense of Serre) of l-adic representations attached to abelian varieties and (more generally) to l-adic cohomology of schemes.