28.10.2022 um 14:15 Uhr in 69/125
George Raptis (Universität Regensburg)
Devissage theorems in algebraic K-theory
A devissage type theorem in algebraic K-theory identifies the K-theory of a Waldhausen category in terms of the K-theories of a collection of Waldhausen subcategories, when a devissage condition about the existence of appropriate finite filtrations is satisfied. Quillen's and Waldhausen's classical theorems of this type express fundamental properties of algebraic K-theory and have many applications. In this talk, I will discuss general aspects of devissage in algebraic K-theory and give an overview of old and new theorems of this type.
01.02.2023 um 14:15 Uhr in 69/E23
Federico Mocchetti (Università degli Studi di Milano/Universität Osnabrück)
MHH_*(F_p): a spectral sequence approach
After a general introduction to stable motivic homotopy theory, we will switch to the study of the homotopy groups of the motivic Hochschild homology spectrum.
A classical result by J. Greenlees proves the existence of a homotopy-analogue of the Serre’s spectral sequence. We will extend it to the motivic setting. This, together with some algebraic results, will allow us to compute the homotopy groups of spectra which are closely related to the motivic Hochschild homology one.
08.02.2023 um 14:15 Uhr in 69/E23
William Hornslien (NTNU Trondheim)
Endomorphism of the projective line
A fundamental problem in algebraic topology is the study of homotopy groups of spheres. In classical topology, the projective line over R is a 1-sphere, and the projective line over C is a 2-sphere. Motivic homotopy theory is a homotopy theory for smooth algebraic varieties, and the projective line is a sphere in this homotopy theory. Due to the algebraic nature of varieties, we can describe all endomorphisms of the projective line, which in turn makes it easier to study its homotopy classes. This is joint work with Viktor Barth, Gereon Quick, and Glen Wilson.