2021

Intercity seminar

11:15–12:00

Remy van Dobben de Bruyn Leiden, Equivalent conjectures on independence of ℓ

The ℓ-adic étale cohomology of a variety is defined in terms of the geometry of ℓ-power degree coverings. Unlike in algebraic topology, there is no integer-valued theory to compare with, leading to a plethora of “independence of ℓ” conjectures for varieties over finite fields. We will survey what is known, and prove that independence of ℓ for Betti numbers is equivalent to two other statements involving algebraic cycles.

14:15–15:00

Margherita Pagano Leiden, An example of a Brauer–Manin obstruction to weak approximation at a prime with good reduction

A way to study rational points on a variety is by looking at their image in the p-adic points. Some natural questions that arise are the following: is there any obstruction to weak approximation on the variety? Which primes might be involved in it? Bright and Newton have proven that for K3 surfaces defined over number fields primes with good ordinary reduction play a role in the Brauer–Manin obstruction to weak approximation.

In this talk I will give an explicit example of this phenomenon. In particular, I will exhibit a K3 surface defined over the rational numbers having good reduction at 2, and for which 2 is a prime at which weak approximation is obstructed.

15:15–16:00

Daan van Gent Leiden, Indecomposable algebraic integers

In algebraic number theory, the finiteness of the Picard group of an order in a number field is generally proved via a lattice argument: the order forms a lattice and every ideal class contains an integral ideal with a small enough non-zero element. In this talk we will consider ℤ̄, the ring of algebraic integers, which is a lattice in a similar sense, and we will treat this lattice as intrinsically interesting. We will state several open problems and some partial results, mainly with regards to the Voronoi polyhedron of ℤ̄. This motivates the study of the indecomposable elements of ℤ̄.

16:30–17:15

Pim Spelier Leiden,

Intercity seminar

11:15–12:00

Peter Stevenhagen Leiden, Elliptic curves and primes of cyclic reduction

14:15–15:00

Charlotte Dombrowsky Leiden, An upper bound for packings on spheres

15:30–16:15

Yukako Kezuka MPIM Bonn, On central L-values of twists of the Fermat elliptic curve

16:15–17:00

Eugenia Rosu TU Darmstadt / Leiden, Twists of elliptic curves with complex multiplication

Intercity seminar / Getaltheorie in het Vlakke Land / Arithmétique en Plat Pays

13:15–14:00

Laurent Berger ENS Lyon, Unlikely intersections for formal groups

14:15–15:00

Michel Rigo Liège, Numeration systems: a link between formal languages and number theory

15:30–16:15

Amita Malik MPIM, Integer partitions analysis

16:30–17:15

Lola Thompson Utrecht, Salem numbers and short geodesics