Seminar Algebra und Topologie

Das Seminar findet normalerweise am Mittwoch in F.13.11, 16:30 - 17:30 statt.
Beteiligte Dozenten: Jens Hornbostel, Sascha Orlik, Kay Rülling, Tobias Schmidt, Britta Späth, Matthias Wendt.

Subramanian: Smith Theory Revisited

The Sullivan conjecture is one of the landmark results in unstable homotopy theory, relating genuine fixed points of a finite p-group action to homotopy fixed points (after p-completion). In this talk, I will explain a new approach to the Sullivan conjecture for C_p-actions using perfect commutative \mathbb{F}_p-algebras.
The key idea is that the tilting functor provides an inverse to the Tate construction in the perfect setting, allowing us to recover the cochains on the genuine fixed-point space from Borel-equivariant cochains. Combining this with Mandell's theorem and the Segal conjecture gives a short proof of the Sullivan conjecture.
This is joint work with Robert Burklund.

Ayoub: On the classicality of the motivic Galois group

The motivic Galois group is naturally a derived affine group scheme. The usual motivic conjectures imply that this group is actually classical, i.e., its Hopf algebra is concentrated in degree zero. I will discuss some work in progress aiming at proving this classicality property.
 

Pieropan: Log geometry and lifting rational points

Determining the image of the set of rational points under a morphism of varieties is a very natural and difficult question. The case where the morphism is geometrically surjective has been studied extensively. From Campana's theory of orbifolds, it follows that over a number field, the image of the set of rational points is contained in the set of Campana points for the orbifold base of the morphism. This first approximation of the image of the set of rational points is refined by Abramovich's theory of firmaments. This talk presents a proof of a claim by Abramovich about lifting firm points under toroidal morphisms in joint work with Herr, Mehidi and Poiret.

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