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, Tobias Schmidt, Britta Späth, Kay Rülling, Matthias Wendt.

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.

Vivien Picard: The construction problem for logarithmic Hodge numbers modulo an integer (Masterkolloquium)

The only linear relations, that the Hodge numbers of smooth projective varieties over an algebraically closed base field of positive characteristic satisfy, are the ones induced by connectedness and by Serre duality. We want to investigate if these are also the only linear relations for the logarithmic Hodge numbers. For this, we will work with ordinary varieties. We will focus on the inner Hodge numbers.

Shuji Saito: Pro-cdh descent for algebraic K-theory of derived schemes

Thanks to a celebrated theorem of Kerz-Strunk-Tamme, algebraic K-theory satisfies the pro-excision for abstract blowup squares of noetherian schemes. The latter property fails for non-noetherian schemes in general. A main result in this talk affirms that algebraic K-theory satisfies the property for (not necessarily noetherian ) qcqs derived schemes.  As an application, we deduce Weibel’s vanishing of negative K-theory for qcqs derived schemes. In the noetherian case, this is due also to Kerz-Strunk-Tamme. This is a joint work with Shane Kelly and Georg Tamme.

• Gästeseminare vergangener Semester