Vortrag
Motivic spectra and universality of algebraic K-theory
Vortrag von Dr. Ryomei Iwasa
Sprecher eingeladen von: Prof. Dr. Joseph Ayoub
Datum: 12.12.22 Zeit: 13.15 - 14.45 Raum: Y27H25
The theory of motives is intended to study various cohomology theories of schemes in a unified way, including étale cohomology, crystalline cohomology, syntomic cohomology, algebraic K-theory, and topological cyclic homology. As spectra are crucial to the study of cohomology theories in algebraic topology, the theory of "motivic spectra" is expected in algebraic geometry. As you know, there is already a widely recognised theory of motivic spectra by Voevodsky. However, many of the aforementioned examples are not representable by motivic spectra in Voevodsky’s sense, because his theory cannot detect infinitesimal thickenings. In this talk, I will propose a more general notion of motivic spectra by which all relevant cohomology theories are representable. I will explain that some of the important results known for Voevodsky’s motivic spectra remain true. Then, as an application, I will explain a universal characterisation of algebraic K-theory of schemes, namely, it is universal among Zariski sheaves of spectra which admit BG_m-action and satisfy projective bundle formula. This talk is based on joint work with Toni Annala and Marc Hoyois.