Belgian-Dutch Algebraic Geometry Day

The 7th edition of this seminar will be held on Friday 14 November 2014, at the University of Amsterdam, Science Park 904.


Minhyong Kim (Oxford)
Non-abelian reciprocity laws and Diophantine geometry
Abstract. We formulate a generalisation of Artin reciprocity to allow non-abelian coefficients. We outline applications to Diophantine geometry.
Mingmin Shen (UvA)
Multiplicative Chow-Künneth decompositions
Abstract. This is joint work with Charles Vial. We will define what a multiplicative Chow-Künneth decomposition is and explain how this induces a bigrading on the Chow ring. I will discuss several examples of varieties with multiplicative CK decomposition.
Jakob Stix (Frankfurt)
Gorenstein orders and abelian varieties over finite fields
Abstract. Thanks to a result of Deligne, the category of ordinary abelian varieties over a fixed finite field can be described in terms of finite free Z-modules equipped with a linear operator F (playing the role of Frobenius) satisfying certain axioms. Deligne's result is based on Serre-Tate canonical lifting. We prove a similar result for the full subcategory of all abelian varieties over the prime field supported on non-real Weil numbers, thereby obtaining a description of non-ordinary isogeny classes in Deligne's spirit. However, we must substitute lifting to characteristic zero by the commutative algebra of Gorenstein orders, because thanks to work of Chai, Conrad and Oort functorial lifting is not always possible. This is joint work with Tommaso Centeleghe (Heidelberg).

As usual, after the lectures we intend to go for an informal dinner in town.


Ben Moonen (Nijmegen), Johannes Nicaise (Leuven), Lenny Taelman (UvA).