:= Immanuel Halupczok

Lehrstuhl für Algebra und Zahlentheorie
Mathematisches Institut
Heinrich-Heine-Universität Düsseldorf
Gebäude 25.22
Universitätsstr. 1
40225 Düsseldorf

Phone: +49 211 81-13189


Lecture notes

Warning: Most lecture notes are written rather quickly and might be full of typpos and other mistakes.

Slides/summaries of some talks

  • 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 (2006)
  • 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 (2007)
  • 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 (2008)
  • Trees of varieties over ℤp
    Assigning trees to subsets of pn; conjecture on the (combinatorial) structure of these trees; associated Poincaré series; some examples where the conjecture holds
    16 slides (2008)
  • RV information of definable sets in valued fields
    Classifying definable sets in valued fields up to "RV-isometry"
    summary; 2 pages (2010)
  • Approximate Subgroups / Isometries in valued fields
    1. an introductory talk to a result by Breuillard-Green-Tao classified subsets of groups
    2. a geometric approach to the rationality of Poincaré series
    summaries of two talks; 2 pages (2013)