Alberto Navarro Garmendia (U Zürich)
Tuesday, June 19, 2018 - 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
Grothendieck's Riemann-Roch theorem compares direct images at the level of K-theory and the Chow ring. After its initial proof at the Borel-Serre report, Grothendieck aimed to generalise the Riemann-Roch theorem at SGA 6 in three directions: allowing general schemes not necessarily over a base field, replacing the smoothness condition on the schemes by a regularity condition on the morphism, and avoiding any projective assumption either on the morphism or on the schemes. After the coming of higher K-theory there was also a fourth direction, to prove the Riemann-Roch also between higher K-theory and higher Chow groups. In this talk we will review recent advancements in these four directions during the last years. If time permits, we will also discuss refinements of the Riemann-Roch formula which takes into account torsion elements.
submitted by Marion Thomma (thomma@math.hu-berlin.de)