Modul: MAT770 Oberseminar: Algebraische Geometrie

## Relative intersection theory and the Riemann-Roch theorem

Talk by Dr. Dennis Eriksson

Speaker invited by: Prof. Dr. Joseph Ayoub

**Date:** 21.11.23 **Time:** 13.15 - 14.45 **Room:** Y27H25

Together in recent work with G. Freixas, we study a relative intersection theory, with values in line bundles, originally introduced by Deligne and developed by e.g. Elkik. Whereas one usually intersects n divisors on an n-dimensional variety and gets a number, here intersects n+1 divisors and gets a line.

It amounts to a categorical refinement of direct images in Chow-theory. We introduce a formalism and categorical framework that allows us to give life to many of the usual intersection theoretic notions to categorified levels.

A great motivation for developing this was to study categorified versions of the Grothendieck-Riemann-Roch theorem, conjectured by Deligne. While being of general interest, it has also turned out to be important in Arakelov theory, algebraic geometry, mirror symmetry, and other fields. I will also report on some partial results in this direction.