| date |
theme |
description |
speaker/notes |
literature |
| 18.10.05 |
Motivating examples |
the two basic examples forthis
Forschungsseminar are 1. local systems on CW-complexes 2. vector bundles on schemes This talk should describe the moduli problems, show that their give rise to an algebraic stack, and that this stacks is not smooth. Then it should give the perspective that derived/homotopical algebraic geometry may lead to better behaved moduli problems and smooth stacks. |
M. Spitzweck/U. Bunke |
[2],[3],[4] |
| 25.10.05 |
Simplicial algebras as a
HA-context |
In this talk simplicial algebras
should be introduced. The goal is to construct a symmetric monoidal
model category of such algebras and to verify the conditions for a
HA-context. The category of simplicial algebras should be related to
the categories of dg-algebras and E_\infty-algebras. |
M. Spitzweck/U. Bunke |
[2],[5] |
| 1.11.05 |
Symmetric spectra as a HA-context |
In this talk a symmetric
monoidal model category of spectra (symmetric spectra) should be
constructed and the properties of a HA-context should be verified. The
relation with E_\infty-spectra should be revied. Furthermore, using
Eilenberg-MacLane spectra symmetric spectra should be related to rings. |
U. Bunke/C. Barwick |
[2],[6] |
| 8.11.05 |
Pre-stacks on model categories |
The global model structure on
the category of simplicial pre-sheaves on a model category should be
introduced. The Yoneda embedding of the model category into the sheaves
should be presented. Finally the localization by the weak equivalences
should be discussed. |
Th. Schick/M. Spitzweck |
[1] |
| 15.11.05 |
Derivations and the cotangent
complex |
The derived derivations in a
HA-context should be introduced. It further should be shown that this
functor is represented by the cotangent complex. The latter should be related to the classical notions. It should be revied how the classical notions of etale, smooth can be characterized in terms of the cotangent complex. |
U. Bunke/C. Barwick |
[2] |
| 22.11.05 |
Topological Hochschild cohomology |
The topological Hoschild
cohomology should be defined in a HA-contex. It should be related
with the cotangent complex. Furthermore, the relations with the
classical Hochschild cohomology for algebras and the topological
Hoschild cohomology in stable homotopy theory should be discussed. |
M. Spitzweck/U. Bunke |
[2],?? |
| 29.11.05 |
Linear algebra in a HA-context |
In this talk further linear
algebra in an HA-context should be discussed, in particular notions
like: -Zariski open embedding and localization -finitely generated module -smooth morphisms -coverings |
C. Barwick/Th. Schick |
[2] |
| 6.12.05 |
Model sites and theit topoi |
The topics for this talk are: -topologies on model and S-categories -hyper covers and pseudo-representable hypercovers -local weak equivalences -the model structure on the category of simplicial presheaves on a model topology adapted to local weak equivalences - the notion of a stack |
C. Barwick/Th. Schick |
[2] |
| 13.12.05 |
Revisiting the motivating
examples |
In this talk the two motivating
examples of the first talk should be extended to the homotopical
setting. It should be shown that they lead to a stack on an
appropriate model site. |
M. Spitzweck/U. Bunke |
[2] |
| 3.1.06 |
Geometric stacks |
The goal of this talk is to
introduce the notion of as geometric stack. We are further interested
in properties of maps between stacks like smoothness. The relation to
the classical notions according to Artin should be given. It should be
shown how a geometric stack leads to a groupoid and can be
represented as a quotient by a groupoid. |
B. Toen/M. Spitzweck |
[2] |
| 10.1.06 |
Smoothness of the stacks in the
examples |
In this talk it should be shown
that the stacks for the extended moduli problems in our examples are
geometric and smooth. |
M. Spitzweck/U. Bunke |
[2] |
| 17.1.06 |
Higher Tannakian duality |
The topics for this talk are: - Tannakian Segal categories - a conjectured duality statement - a brave noew gerbe of fibre functors |
C. Barwick/M. Spitzweck |
[7] |
| 24.1.06 |
Derived representability |
The derived representability
theorem according to Luries thesis should be reviewed. |
C. Barwick/U. Bunke |
[8] |
| 31.1.06 |
tmf in an HAG-context |
Some details about the
construction of topological modular forms in the homotopical algebraic
geometry setting should be presented. |
???/??? |
|
| 7.2.06 |
reserve |
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