Mattia Tolpo, University of British Columbia
“Parabolic sheaves, root stacks and the Kato-Nakayama space”
Parabolic bundles on a punctured Riemann surface were introduced by Mehta and Seshadri in the ’80s, in relation to unitary representations of its topological fundamental group. Their definition was generalized, in several steps, to a definition over an arbitrary logarithmic scheme due to Borne and Vistoli, who also proved a correspondence with sheaves on stacks of roots. I will review these constructions, and push them further to the case of an ”infinite” version of the root stacks. Towards the end I will discuss a comparison result (for log schemes over the complex numbers) between this ”infinite root stack” and the so-called Kato-Nakayama space, and hint at some work in progress about relating sheaves on this latter space to parabolic sheaves with arbitrary real weights.
MC 5403