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Guest seminar winter 2017/18

Guest seminar "Arithmetic Geometry"

Time: Thursdays, 2pm-4pm

Place: SR 032 Arnimallee 6


Date Speaker(s)
October 12

Richard Griffon

Title: A Brauer-Siegel theorem for Fermat surfaces
over finite fields

The classical Brauer-Siegel theorem gives asymptotic upper and lower bounds on the product of the class-number 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 Néron-Severi 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.

October 19

Markus Röser (Hannover)

Mini-course non-abelian Hodge theory

October 26  

Markus Röser (Hannover)

Mini-course non-abelian Hodge theory

November 2 (1/2) Yves André (Paris)

Title: Perfectoid spaces and the homological conjectures

November 2 (2/2) Oliver Braunling (Freiburg)

Title: K-theory of locally compact (instead of finitely generated) modules

We discuss a generalization of a March 2017 theorem of Dustin Clausen,
following footsteps of A. Weil. Come if you want to enjoy the magical
wonders of the interaction of K-theory, LCA groups and basic number

November 9

Jungkai CHEN (National Taiwan University)

Title: Pluricanonical maps of higher dimensional varieties.

Pluricanonical maps are  natural maps associated to projective varieties. It is well-known that m-th canonical maps stabilized birationally as long as m is large enough and divisible. It is interesting to know explicitly the structure  of the stablized map, as well as the geometric description of the map.
We will survey some recent development of threefolds and higher dimensional varieties along this direction.

 November 16

(Special Time: 10:30 am sharp, SR140/A7)


Gereon Quick (Norwegian University of Science and Technology)

Title: Examples of non-algebraic classes in the Brown-Peterson tower

It is a classical problem in algebraic geometry to decide whether a class in the singular cohomology of a smooth complex variety X is algebraic, i.e. if it can be realized as the fundamental class of an algebraic subvariety of X. Given a motivic spectrum E, one can ask a similar question: which classes in the corresponding topological E-cohomology of X come from motivic/algebraic classes? In my talk, I will discuss some obstructions for such classes to being algebraic and construct examples of non-algebraic classes for the tower of Brown-Peterson spectra.  

 November 23

Michael Gröchenig

A short talk off-seminar.

November 30.

(Time: 15:00  Sharp) 

Shane Kelly

Title: Introduction to (stable) motivic homotopy theory. 

 11. January

Marco d'Addezio

Title: Lisse sheaves and F-isocrystals. 

 18. January

Michel van Garrel (University of Hamburg)

Title: 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 re-prove 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

Title: p-adic integration for Hitchin systems