Michael Stoll
Michael Dettweiler
Mathematisches Institut
Universität Bayreuth
95440 Bayreuth, Germany

Oberseminar Arithmetische Geometrie

Preliminary Schedule WS 2014/15

    Tuesday, 16:15-18:00   in S75
  7. 10. 2014   Organizational meeting
  14. 10. 2014   no seminar (Number Theory Group in Luminy)
  21. 10. 2014   no seminar (Important meeting)
  24. 10. 2014 Michael Stoll: Simultaneous torsion x-coordinates in the Legendre family of elliptic curves
  14-16, S80
  4. 11. 2014 Benjamin Collas: Arithmetic of stack inertia in moduli spaces of curves
  11. 11. 2014 Michael Kiermaier: Subspace codes and q-analogs of combinatorial designs
  18. 11. 2014 Joachim König (Würzburg): The inverse Galois problem and explicit computation of Hurwitz spaces

By work of Fried, Völklein et al., the regular inverse Galois problem is famously linked to questions about the existence of rational points on certain moduli spaces. In some cases, this existence can be proven by theoretical means; a famous example is Matzat's realization of M24 over Q.

In cases where the theoretical criteria do not work, little is known. I will present techniques for explicit computation of moduli spaces and use them to produce algebraic equations for Hurwitz spaces belonging to the Mathieu group M23, the last remaining sporadic group not yet realized as a Galois group over Q. Suitable rational solutions for these equations would lead to M23-realizations over Q.

Still, finding such points — or proving that they do not exist — remains a difficult problem. I will discuss some approaches that might help.

Similar methods may be used to classify monodromy groups of rational functions over Q. As partial results, I will present new polynomials for several almost simple groups, e.g. the first explicit polynomials with regular Galois groups PSL5(2) and PSL3(4) over Q.

  25. 11. 2014 Stefan Reiter: On G2-rigid local systems
  2. 12. 2014 Michael Stoll: Computing canonical heights on genus 2 Jacobians in polynomial time
  9. 12. 2014 Julian Tenzler:
On trace functions on étale sheaves
Talk canceled, moved to January!
  16. 12. 2014 Andreas Kühn: Torsion subgroups of hyperelliptic Jacobians
  13. 1. 2015 Julian Tenzler: On trace functions on étale sheaves
  23. 1. 2015 Benjamin Collas: Motives: from Geometry to Homotopy Theory
  14-16, S78
  30. 1. 2015 Julian Tenzler: On trace functions on étale sheaves, II
  12-14, room TBD
  9. 4. 2015 Mark Watkins (Sydney): Number Theory and Algebraic Geometry in Magma
  10-12, S80

Schedule Sommersemester 2014
Michael Stoll,  March 31, 2015