Infinite root stacks of logarithmic schemes -- Angelo Vistoli, April 18, 2014

I will report on joint work with Mattia Talpo, building on previous joint work with Niels Borne. With every fine saturated logarithmic scheme, we associate a proalgebraic stack, called its infinite root stack; many questions in logarithmic geometry admit useful translations in terms of infinite root stacks. After a short introduction to logaritmic geometry I will describe some of the main properties of the infinite root stack, and explain why quasi-coherent sheaves on a logarithmic scheme should be defined as a quasi-coherent sheaves on the infinite root stack, and how these quasi-coherent sheaves admit a natural interpretation as parabolic sheaves. I will conclude by giving a brief account of Mattia Talpo's work on the moduli theory of stable parabolic coherent sheaves.