FB 6 Mathematik/Informatik

Institut für Mathematik


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WS 2016/2017

01.11.2016 um 14:15 Uhr in 69/E15:

Oliver Röndigs (Universität Osnabrück)

Overview

15.11.2016 um 14:15 Uhr in 69/E15:

Oliver Röndigs (Universität Osnabrück)

Motivic homotopy theory

22.11.2016 um 14:15 Uhr in 69/E15:

Alexey Ananyevskiy (St. Petersburg State University)

Rigidity for stable motivic homotopy groups

29.11.2016 um 14:15 Uhr in 69/E15:

Martin Frankland (Universität Osnabrück)

Voevodsky's motivic Eilenberg-MacLane spectrum

13.12.2016 um 14:15 Uhr in 69/E15:

Konrad Voelkel (Universität Osnabrück)

Geometric classifying spaces and their motivic cohomology

03.01.2017 um 14:15 Uhr in 69/E15:

Anandam Banerjee (IISER Mohali, India)

Tensor Structure on Smooth Motives

Levine constructed the category of smooth motives over a base as a DG enriched category. To elaborate, he defined a DG category whose homotopy category is equivalent to the full subcategory of motives over a base-scheme S generated by the motives of smooth projective S-schemes, assuming that S is itself smooth over a perfect field. However, having a tensor structure on his category required rational coefficients. After briefly describing Levine's construction, I will explain how to provide a weaker structure on his DG category that does give a tensor structure on the category of smooth motives under certain conditions on S.

10.01.2017 um 14:15 Uhr in 69/E15:

Sabrina Syed (Universität Osnabrück)

The classical Steenrod algebra and its dual

17.01.2017 um 14:15 Uhr in 69/E15:

Manh Toan Nguyen (Universität Osnabrück)

The motivic Steenrod algebra and its dual

18.01.2017 um 14:15 Uhr in 69/E23:

Anandam Banerjee (IISER Mohali, India)

Frames motives and resolutions of suspension 1-spectra

Garushka and Panin introduced the triangulated category of framed motives following Voevodsky's theory of framed sheaves. I will briefly sketch their construction and describe the framed motive of a smooth algebraic variety in this category. Then, I will also talk about the motivic quasi-fibrant replacement of the suspension 1-spectra of a smooth scheme in this setting.

24.01.2017 um 14:15 Uhr in 69/E15:

Markus Spitzweck (Universität Osnabrück)

Extensions to positive characteristic and Dedekind domains

07.02.2017 um 14:15 Uhr in 69/E15:

Dr. Yaël Frégier (Université d'Artois, Lens)

How to get the formulas defining morphisms up to homotopy?

The aim of this talk is to explain classical techniques enabling to derive the formulas defining homotopy maps betwen algebraic structures. In this formalism the algebraic structures themselves can be understood as homological coderivations of some coalgebras, while the homotopy morphisms are given by the coalgebra morphisms which intertwine the homological coderivations. We will  in particular concentrate on the case of associative and Lie algebras. We will also give a hint on how this generalizes to algebras over arbitrary Koszul quadratic operads.

14.02.2017 um 14:15 Uhr in 69/E15:

Dr. Florian Strunk (Universität Regensburg)

A descent result for algebraic K-theory

Given an abstract blow-up square of finite dimensional noetherian schemes, one may ask whether there is an associated Mayer-Vietoris sequence on algebraic K-theory groups. Even though this is not the case in general, there exists such a Mayer-Vietoris sequence for K-theory pro-groups obtained by infinitesimal thickenings inside the abstract blow-up square. Combining this result with a flatification technique, we obtain Weibel’s conjecture on the vanishing of negative K-groups. This in joint work with Moritz Kerz and Georg Tamme.