Gästeseminar Wintersemester 2017/18
Gästeseminar "Arithmetische Geometrie"
Zeit: Donnerstags, 14:1515:15 Uhr
Ort: SR 032 in Arnimallee 6
Vorträge:
Titel:
Datum  Vortragende(r) 

12. October* 
Richard Griffon (Leiden) Titel: A BrauerSiegel theorem for Fermat surfaces The classical BrauerSiegel theorem gives asymptotic upper and lower bounds on the product of the classnumber times the regulator of units of a number field in terms of its discriminant. In this talk, I will describe an analogous result in a more geometric context. Namely, for a Fermat surface F over a finite field, we consider the product of the order of its Brauer group (which is known to be finite) by the Gram determinant of a basis of its NéronSeveri group for the intersection form, and we describe the growth of that product in terms of the geometric genus of F when the latter grows to infinity. As in the classical setting, the proof of the asymptotic estimate is rather analytic: it relies on obtaining asymptotic bounds on the size of the ``residue’’ of the zeta function of F at its pole at s=1. 
19. Oktober 
Markus Röser (Hannover) Minicourse nonabelian Hodge theory 
26. Oktober 
Markus Röser (Hannover) Minicourse nonabelian Hodge theory 
2. November (1/2)  Yves André (Paris) Titel: Perfectoid spaces and the homological conjectures 
2. November (2/2) 
Oliver Braunling (Freiburg) Titel: Ktheory of locally compact (instead of finitely generated) modules We discuss a generalization of a March 2017 theorem of Dustin Clausen, 
9. November 
Jungkai CHEN (National Taiwan University) Titel: Pluricanonical maps of higher dimensional varieties.

16. Novemeber (Sonderzeit: 10:30 genaue Zeit, A7/SR140) 
Gereon Quick (Norwegian University of Science and Technology) Titel: Examples of nonalgebraic classes in the BrownPeterson tower 
23. November 
Michael Gröchenig Description: A short talk offseminar. 
30. November (Sonderzeit: 15:00 genaue Zeit) 
Shane Kelly Titel: Introduction to (stable) motivic homotopy theory. 
11. Januar 
Marco d'Addezio Titel: Lisse sheaves and Fisocrystals. 
18. Januar 
Michel van Garrel (University of Hamburg) Titel: A constructive approach to a conjecture by Voskresenskii Voskresenskii conjectured that stably rational tori are rational. Klyachko proved this assertion for a wide class of tori by general principles. In this joint work with Mathieu Florence, we reprove Klyachko’s result by providing simple explicit birational isomorphisms. 
25. Jan. 
Giulio Bresciani (Scuola Normale Superiore, Pisa) Title: The dimensional section conjcture. Abstract: Vistoli observed that, if Grothendieck's section conjecture is true, there should be some notion of dimension such that for an hyperbolic curve over a field finitely generated over Q the space of sections has dimension 1. If one could prove this, it would give a dimensional obstruction to the existence of sections. We propose such notion as a modification of essential dimension, and make some steps toward proving that this dimension is 1 for the space of sections of P^1 minus three points. 
1. Feb. 
Michael Gröchenig Titel:padic integration for Hitchin systems 
* SR 031 in Arnimallee 7