Immanuel Halupczok - Vortragsfolien

Mengen, die mich enthalten:

Immanuel Halupczok	∈	Institut für Mathematische Logik und Grundlagenforschung			⊂	Fachbereich Mathematik und Informatik	⊂	Westfälische Wilhelms-Universität Münster
	∈	Project A4: Algebraic groups and model theory	⊂	SFB 878 Groups, Geometry & Actions	⊂

A tree associated to the cusp curve X³ = Y² in Z₃; see Trees of definable sets in Z_p for details.

Main topic: Model theory and arithmetic geometry in henselian valued fields

A strong kind of Whitney stratifications in henselian valued fields
Motivic integration: new transfer principles and some applications to representation theory of p-adic groups

Measures on perfect PAC fields with pro-cyclic Galois group
Dimension and measure on pseudo-finite fields; generalization to other perfect PAC fields
20 slides
Motives for some PAC fields
Assigning motives to definable sets over pseudo-finite fields; generalization to other PAC fields with pro-cyclic Galois group; maps between Grothendieck ring of different such theories
5 pages of notes
Definable sets in pseudo-finite fields
Invariants for pseudo-finite fields obtained by counting over finite fields (in particular: dimension and measure); in a fixed pseudo-finite field and for the theory of all pseudo-finite fields; maps between different Grothendieck rings and generalization to theories where counting is not possible.
22 slides
Trees of varieties over ℤ_p
Assigning trees to subsets of ℤ_pⁿ; conjecture on the (combinatorial) structure of these trees; associated Poincaré series; some examples where the conjecture holds
16 slides