Tuesday, June 25, 2019 - 13:15
Humboldt-Universität zu Berlin, Institut für Mathematik
Rudower Chaussee 25, 12489 Berlin-Adlershof, Raum 006, Haus 3, Erdgeschoss
Forschungsseminar Arithmetische Geometrie
Prof. Jürg Kramer / Prof. Thomas Krämer
We extend McMullen's polytope algebra to the so called convex set algebra. We show that the convex set algebra embeds in the projective limit of the Chow cohomology rings of all smooth toric compactifications of a given torus, with image generated by the classes of all nef toric b-divisors. It follows that the convex-set algebra can be viewed as a universal ring for intersection theory of nef toric 𝑏-cocycles on the toric Riemann-Zariski space. We further discuss some applications of this viewpoint towards a combinatorial interpretation of non-archimidean Arakelov theory of toric varieties over discretely valued fields in the sense of Bloch-Gillet-Soulé.
submitted by Marion Thomma (thomma@math.hu-berlin.de, 2093-5815)