The Grothendieck-Witt theory of quadratic functors
Emanuele Dotto (University of Warwick)
Monday 2nd March, 2020 16:00-17:00 Maths 311B
The Grothendieck-Witt spectrum of a ring is an object constructed from the forms (quadratic, symmetric, or symplectic) on that ring, in a way analogous to Quillen's algebraic K-theory.
I will talk about joint work with B. Calmès, Y. Harpaz, F. Hebestreit, M. Land, K. Moi, D. Nardin, T. Nikolaus & W. Steimle, where we extend this construction to stable infinity categories equipped with a suitable quadratic functor, which encodes a formal notion of forms on the objects of the category.
This general framework allows us to establish a general relationship between Grothendieck-Witt theory and Ranicki-Wall's L-theory generalizing a theorem of Schlichting, and to reprove and improve some classical results on the Grothendieck-Witt spectrum of rings.