An isomorphism of > motivic Galois groups
Friday, 2.5.14, 10:15-11:15, Raum 404, Eckerstr. 1
Symmetries of the Hesse pencil with applications
Friday, 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
Friday, 23.5.14, 10:15-11:15, Raum 404, Eckerstr. 1
Tilting Theory via Stable Homotopy Theory
Friday, 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.