ABOUT EVENT

In 1980, Weibel asked the following cohomological dimension-esque question. If R is a Noetherian ring of Krull dimension d, does K_{n}(R) vanish for all n < -d? This stimulated four decades of research, resolving various special cases, then the problem as stated, then generalisations.

In this talk we do the opposite. We discuss a generalisation where the conjecture fails. Specifically, for every n ≥ 2 we give an example of a (necessarily non-noetherian) ring R of Krull dimension 1 with K_{-n}(R) ≠ 0. The idea, roughly, is to find an infinite polyhedron inside the Riemann-Zariski space of ?^n
by repeatedly blowing up all faces of an initial polyhedron. Then contracting this infinite polyhedron produces the desired example.

Este seminario, abierto a todo el público interesado, es organizado por los miembros del grupo de Geometría No Conmutativa. Las reuniones son los martes a las 10:00hs, vía Zoom (para recibir las coordenadas escribir a gtartaglia arroba mate.unlp.edu.ar)