Schedule and Abstracts
Schedule:
- Monday
- 10h-11h: Kahn I
- 11h-11h15: coffee
- 11h15-12h15: Kahn II
- 12h30-14h: Lunch
- 15h-16h: Hoffmann I
- 16h-16h30: coffee
- 16h30-17h30: Zainoulline
- Tuesday
- 10h-11h: Hoffmann II
- 11h-11h15: coffee
- 11h15-12h15: Hoffmann III
- 12h30-14h: Lunch
- 15h-16h: Garibaldi I
- 16h-16h30: coffee
- 16h30-17h30: Shripad
- Wednesday
- 9h-10h: Kahn III
- 10h-10h30: coffee
- 10h30-11h30: Garibaldi II
- 11h30-11h45: coffee
- 11h45-12h45: Garibaldi III
- 13h-14h: lunch
The wednesday afternoon is free!
- Thursday
- 10h-11h: Hoffmann IV
- 11h-11h15: coffee
- 11h15-12h15: Kahn IV
- 12h30-14h: lunch
- 15h-16h: Garibaldi IV
- 16h-16h30: coffee
- 16h30-17h30: Calmès
- Friday
- 9h-10h: Garibaldi V
- 10h-10h30: coffee
- 10h30-11h30: Kahn V
- 11h30-11h45: coffee
- 11h45-12h45: Hoffmann V
- 13h-14h: lunch.
Courses:
- Course of Skip Garibaldi
- Title: Cohomological invariants
- Abstract: The determinant and
Hasse-Witt invariant of quadratic forms are two examples of
cohomological invariants. The interesting fact is that one
can--sometimes!--explicitly describe all the cohomological
invariants. This was done for quadratic forms and several other
examples in Serre's portion of the book "Cohomological invariants
in Galois cohomology". These lectures will summarize the necessary
tools and apply them in various cases. We will emphasize examples
not covered in Serre's lectures, including Rost's results on
invariants of Spin groups.
- Course of Detlev
W. Hoffmann
- Title: Quadratic forms in
characteristic 2
- Abstract: For many years, much of
the research on quadratic forms has focussed up to sporadic
exceptions on the case of characteristic not 2. However, over the
past few years, the theory of quadratic forms in the case 2=0 has
experienced a resurgence in the work of Arason, Aravire, Baeza,
Hoffmann, Jacob, Knebusch, Laghribi etc. In this lecture series,
we present some of these recent developments in the algebraic
theory of quadratic forms in characteristic 2. Topics may include
(if time permits) specialization and generic splitting of
quadratic forms, exact sequences of Witt groups, the behaviour of
quadratic forms and cohomology (Ã la Kato) under field
extensions, in particular extensions given by function fields of
quadratic forms.
- Course of Bruno
Kahn
- Title: "1-motifs"
- Abstract: Le mini-cours, concernant un
travail en collaboration avec Luca Barbieri-Viale, couvrira les
thèmes suivants:
- 1-motifs de Deligne (sur un corps parfait).
- 1-motifs avec torsion (Barbieri-Viale-Rosenschon-Saito).
- La catégorie dérivée des 1-motifs.
- Lien avec les motifs étales de Voevodsky.
- Applications: faisceaux 1-motiviques, théorème de Roitman,
conjecture de Deligne.
Talks:
- Talk of Baptiste Calmès
- Title: A push-forward for the coherent
Witt groups of schemes (joint work with Jens Hornbostel)
- Abstract: Anyone studying quadratic
forms knows the Witt group of a field. Witt groups of schemes are
less well known, though they probably can be quite useful, even to
provide information about the Witt group of a field. Paul Balmer
has given a very workable definition of higher Witt groups in
terms of triangulated categories with dualities. He proved
important properties such as a long exact sequence of localization
in this abstract framework. He applied this mainly to the derived
category of locally free sheaves on a scheme, recovering the
classical definition of Knebush in this case. One useful tool that
he did not provide (in the framework of schemes) is a push
forward, along a certain class of morphisms. We will explain how
this can be defined in an abstract framework, and then apply it to
the coherent Witt groups of schemes using results from the theory
of Grothendieck duality. We will give a few examples of how it can
be useful.
- Talk of Shripad Garge
- Title: On excellence of $F_4$
- Abstract: An algebraic group $G$
defined over a field $k$ is said to be excellent if for any
extension $L$ of $k$ the anisotropic kernel of the group $G
\otimes_k L$ is defined over $k$. This notion was introduced by
Kersten and Rehmann. The excellence properties of some groups of
classical type have been studied so far and it follows easily that
a group of type $G_2$ is excellent over any field.
We prove that a group of type $F_4$ is also excellent over any
field $k$ of characteristic other than 2 and 3.
- Talk of Kirill Zainoulline
- Title: On canonical p-dimensions of
algebraic groups
- Abstract: We compute all p-canonical
dimensions of (split) linear algebraic groups using p-exceptional
degrees invented by V.Kac in the beginning of 80-s.