The Bielefeld Algebraic and Arithmetic Geometry Seminar 2022

Welcome to the website of the Bielefeld Algebraic and Arithmetic Geometry Seminar! For more information, please contact one of the organizers: Claudia Alfes-Neumann, Eike Lau, Michael Spiess, Charles Vial, and Thomas Zink.

Talks

Wednesday 28 June, 2023
15:00	T2-220	Tobias Kreutz (Bonn) TBA [Abstract] TBA
16:45	T2-213	Matthew Honnor (KCL) TBA [Abstract] TBA
Wednesday 14 June, 2023
15:00	T2-220	TBA TBA [Abstract] TBA
16:45	T2-213	TBA TBA [Abstract] TBA
Wednesday 31 May, 2023
15:00	T2-220	TBA TBA [Abstract] TBA
16:45	T2-213	TBA TBA [Abstract] TBA
Wednesday 10 May, 2023
15:00	T2-220	Javier Carvajal-Rojas (EPFL and KU Leuven) TBA [Abstract] TBA
16:45	T2-213	TBA TBA [Abstract] TBA
Wednesday 26 April, 2023
15:00	T2-220	TBA TBA [Abstract] TBA
16:45	T2-213	TBA TBA [Abstract] TBA
Wednesday 5 April, 2023
15:00	T2-220	TBA TBA [Abstract] TBA
16:45	T2-213	TBA TBA [Abstract] TBA
Wednesday 18 January, 2023
15:00	T2-220	Sabrina Pauli (Essen) A quadratically enriched Bézout theorem for tropical curves [Abstract] In enumerative geometry one counts the number of solutions to geometric questions. Classically, this is done over an algebraically closed field. Results from motivic homotopy theory allow to study these questions over an arbitrary field k and get a meaningful answer. One powerful tool to solve questions in enumerative geometry is the use of tropical methods: ``Tropicalization" turns algebraic varieties into polytopes and allows to solve these questions using merely combinatorics. In my talk I will present of one of the first examples of how to use tropical geometry for questions in enumerative geometry over k, namely a proof of the quadratically enriched Bézout's theorem for tropical curves.
16:45	T2-213	Mauro Varesco (Bonn) The Hodge conjecture for powers of K3 surfaces. [Abstract] In this talk, I will present some techniques that have proven to be effective in the study of the Hodge conjecture for powers of K3 surfaces. I will recall the construction of Kuga-Satake varieties and how it can be used to prove the Hodge conjecture for powers of K3 surfaces in some four-dimensional families. This talk is based on the paper [V]. [V] Varesco, M.: The Hodge conjecture for powers of K3 surfaces of Picard number 16. arXiv:2203.09778
Wednesday 14 December, 2022
16:15	T2-213	Sebastian Bartling (Essen) On the étale cohomology of the Fargues-Fontaine curve [Abstract] The Fargues-Fontaine curve associated to a p-adic field and an algebraically closed complete field in characteristic p behaves in many regards like a smooth projective curve over an algebraically closed field; this predicts a certain behavior of its étale cohomology (e.g. the étale cohomological dimension should be two), which was formulated in conjectures of Fargues. I will explain how to handle these conjectures in the prime to p torsion case and state what I know how to prove in the p-torsion case.
Wednesday 19 October, 2022
15:30	V5-148	Salvatore Floccari (Hanover) Sixfolds of generalized Kummer type and K3 surfaces [Abstract] I will explain a construction which associates to any hyper-Kähler sixfold K of generalized Kummer type a hyper-Kähler manifold of K3^[3] type. When K is projective, the associated variety is birational to a moduli space of sheaves on a uniquely determined K3 surface. As application of this construction I will show that the Kuga-Satake correspondence is algebraic for many K3 surfaces of Picard rank 16.
17:00	T2-213	Daiki Kawabe (Tohoku) Chow motives of genus one fibrations [Abstract] Genus 1 fibrations play a central role in the classification of surfaces. Let f : X -> C be a genus 1 fibration from a surface to a curve. Then there is a Jacobian genus 1 fibration j : J -> C that satisfies some good properties. In this talk, we prove that the motive of $X$ is isomorphic to the motive of J. As an application, we prove motivic finite-dimensionality for surfaces not of general type with geometric genus 0. This can be regarded as a generalization of Bloch-Kas-Lieberman's result to arbitrary characteristic.

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Seminars

Conference

The Bielefeld Algebraic and Arithmetic Geometry Seminar 2022

Talks

Wednesday

28 June, 2023

Wednesday

14 June, 2023

Wednesday

31 May, 2023

Wednesday

10 May, 2023

Wednesday

26 April, 2023

Wednesday

5 April, 2023

Wednesday

18 January, 2023

Wednesday

14 December, 2022

Wednesday

19 October, 2022