Tuesday, November 27, 2018 - 13:15
HU, Institut für Mathematik
Rudower Chaussee, 12489 Berlin-Adlershof, 3.006, Erdgeschoss
Forschungsseminar "Arithmetische Geometrie"
Prof. Dr. Jürg Kramer, Prof. Dr. Thomas Krämer
In 1957 Atiyah classified all vector bundles on elliptic curves for an algebraically closed ground field. Moreover, for the characteristic 0 case he completely described the multiplicative structure, i.e. the behavior of the tensor product. In this talk we review the essential results due to Atiyah and will interpret them in the light of Tannakian categories. Namely, allowing only morphisms of vector bundles on elliptic curves that respect the Harder-Narasimhan filtration leads to a neutral Tannakian category. For characteristic 0 we discuss some properties of the corresponding affine group scheme and give complete classifications of certain Tannakian sub-categories. Finally, some known results for the characteristic p case are stated and questions for future research will be formulated.
submitted by Kristina Schulze (schulze@math.hu-berlin.de)