An isomorphism of > motivic Galois groups
Freitag, 2.5.14, 10:15-11:15, Raum 404, Eckerstr. 1
Symmetries of the Hesse pencil with applications
Freitag, 16.5.14, 10:15-11:15, Raum 404, Eckerstr. 1
The Hesse normal form t(x^3+y^3+z^3)+uxyz=0 allows an efficient implementation of the arithmetic on an elliptic curve and immediately exhibits the 9 inflection points in characteristic different from 3.\nFurthermore Artebani and Dolgachev have shown that the group of projective transformations leaving the Hesse pencil invariant can be realized as a group of automorphisms on a singular K3 surface (i.e. one with Picard number 20 in characteristic 0). I intend to demonstrate the\nconstruction of one such surface.
Minkowski decompositions
Freitag, 23.5.14, 10:15-11:15, Raum 404, Eckerstr. 1
Tilting Theory via Stable Homotopy Theory
Freitag, 30.5.14, 10:15-11:15, Raum 404, Eckerstr. 1
Tilting theory is a derived version of Morita theory.\nIn the context of quivers Q and Q' and a field k, this ammounts to looking for conditions which guarantee that the derived categories of the path algebras D(kQ) and D(kQ') are equivalent as triangulated categories.\n\nIn this project (which is j/w Jan Stovicek) we take a different approach to tilting theory and show that some aspects of it are formal consequences of stability. Slightly more precisely, we show that certain tilting\nequivalences can be lifted to the context of arbitrary stable derivators. Plugging in specific examples this tells us that refined versions of these tilting results are also valid over arbitrary ground rings, for quasi-coherent modules on a scheme, in the differential-graded context, and also in the spectral context.
Algebraic cycles of abelian schemes
Freitag, 13.6.14, 10:15-11:15, Raum 125, Eckerstr. 1
Let X be a variety and consider the cycle class map, which maps the Chow groups of X to the cohomology groups of X. Hodge or Tate conjectures predict what should be the image of such a map, and Bloch-Beilinson-Murre conjecture predicts some structures on the kernel. We will investigate these conjectures when X is an abelian scheme, and especially when it is the universal abelian scheme over a PEL Shimura variety
Filtering the Grothendieck spectrum of varieties
Freitag, 20.6.14, 10:15-11:15, Raum 404, Eckerstr. 1
The monodromy group of stratified bundles
Freitag, 4.7.14, 10:15-11:15, Raum 404, Eckerstr. 1
On a variety over a field of positive characteristic a stratified bundle is exactly what a flat connection is on a smooth manifold. Moreover, via the theory of Tannakian categories one can endow a stratified bundle with a monodromy group, in parallel with the complex case. We will see how this group varies in smooth families, proving a strong form of the positive equicharacteristic p-curvature theorem proposed by Esnault and Langer.
The generalized Lipman-Zariski problem
Freitag, 11.7.14, 10:15-11:15, Raum 404, Eckerstr. 1
The order of the reductions of points on algebraic groups
Freitag, 18.7.14, 10:15-11:15, Raum 404, Eckerstr. 1
Ein Theorem von Borcherds im Fall klassischer Modulformen
Freitag, 25.7.14, 10:15-11:15, Raum 404, Eckerstr. 1
Autormorphisms of Curves
Mittwoch, 10.9.14, 14:00-15:00, Raum 404, Eckerstr. 1