Motives, quadratic forms and arithmetic

Session

Thursday morning

Oct 27, 2022, 9:30 AM

Louvre Lens Vallée

1. Quadratic counts of twisted cubic curves on hypersurfaces and complete intersections in a projective space

Marc Levine (Universität Duisburg-Essen)

10/27/22, 9:30 AM

Early on in the development of Gromov-Witten theory, Ellingsrud and Strømme computed the number of twisted cubic curves on hypersurfaces and complete intersections of appropriate (multi-)degree. With Sabrina Pauli, we adapt their method to give a refinement to a ``count’ landing in the Grothendieck-Witt ring of quadratic forms; the rank recovers the classical count, while the signature gives...

12. Representability of Hermitian K-theory in the homotopy category of schemes

Baptiste Calmes

10/27/22, 11:00 AM

This is a report on joint work with Yonatan Harpaz and Denis Nardin.

Hermitian K-theory and motivic homotopy theory enjoy a fruitful relationship, in particular through the quadratic nature of morphisms in the latter, epistomized by the theorem of Morel relating the endomorphisms of the unit sphere with Milnor-Witt K-theory.

A recent definition of Hermitian K-theory in terms of stable...