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WS 2018/2019
23.10.2018 um 14:15 Uhr in 69/117:
Maria Yakerson (Universität Duisburg-Essen)
How to encode transfers in motivic homotopy theory
Voevodsky’s approach to constructing the (derived) category of motives starts with introducing so called presheaves with transfers. Later Calmès and Fasel added extra data of quadratic forms to this construction, by considering presheaves with Milnor-Witt transfers. We will show that these transfers are examples of a more general construction of E-transfers, defined for any motivic ring spectrum E. We will also discuss relation of E-transfers with framed transfers, and some consequences for understanding the category of E-modules.
This is joint work with Elden Elmanto, Marc Hoyois, Adeel Khan and Vladimir Sosnilo
06.11.2018 um 14:15 Uhr in 69/117:
Elmiro Vetere (Universität Freiburg)
Quasi-coherent cohomology of log schemes
This talk will be about the cohomological aspects of Logarithmic geometry. We will define the Kummer log etale site and the (full) log etale site and we will compare their cohomologies to classical etale cohomology, for schemes of finite type over ℂ. We will also talk about log blow-ups, log regularity and how rational singularities appear in this context.
13.11.2018 um 14:15 Uhr in 69/117:
Ilia Pirashvili (Universität Osnabrück)
Axiomatisation of the (étale) fundamental groupoid
The Galois group and the Poincaré group, which were unified by the works of Grothendieck, are of course very imporant invariants. However, it's difficult to state 'what's so special about them'. Indeed, there exists no axiomatic definition of the fundamental group.
In this talk, we will discuss something very closely related. Namely, the universal property of the fundamental groupoid. The latter can be thought of as a 'simultanious collection of fundamental groups at every connected component'. We will give an axiomatisation of the fundamental groupoid (both topological and étale if time permits) using the Seifer-van Kampen theorem, and tools from 2-category theory.
We will finially discuss some of the implications of these results, both from a conceptual- as well as calculatory viewpoint.
11.12.2019 um 14:15 Uhr in 69/117:
Viktor Tabakov (Freie Universität Berlin)
Milnor-Witt K-theory of finite fields
The main goal of the talk will be the computation of Milnor-Witt K-theory of a finite field when the characteristic is not equal to 2. This can be done by generalizing the proof for Milnor K-theory, which also will be given in the talk. If time permits, we will discuss necessary parts of the theory of quadratic forms over a field.
