Seminar Darstellungstheorie

Das Seminar Darstellungstheorie findet normalerweise dienstags, 14.15 - 15.15 Uhr in G.13.18 statt.

Beteiligte Dozenten: Sascha Orlik, Kay Rülling, Tobias Schmidt, Britta Späth.

Niels Feld: Perverse homotopy heart of stable motivic homotopy and Milnor-Witt cycle modules

In the nineties, Voevodsky proposed a radical unification of algebraic and topological methods. The amalgam of algebraic geometry and homotopy theory that he and Fabien Morel developed is known as motivic homotopy theory. Roughly speaking, motivic homotopy theory imports methods from simplicial homotopy theory and stable homotopy theory into algebraic geometry and uses the affine line to parameterize homotopies. Voevodsky developed this theory with a specific objective in mind: prove the Milnor conjecture. He succeeded in this goal and won the Fields Medal for his efforts in 2002.
In this talk, I will present an ongoing project in collaboration with Frédéric Déglise and Fangzhou Jin where we realize Ayoub's conjectural program showing that the heart of the motivic stable homotopy category over appropriate base schemes can be related to a suitable version of relative Milnor-Witt modules.

Julian Quast: On local Galois deformation rings

In joint work with Vytautas Paškūnas, we show that the universal framed deformation ring of an arbitrary mod p representation of the absolute Galois group of a p-adic local field valued in a possibly disconnected reductive group G is flat, local complete intersection and of the expected dimension. In particular, any such mod p representation has a lift to characteristic 0. The work extends results of Böckle, Iyengar and Paškūnas in the case G=GL_n. We give an overview of the proof of this main result.