Description:

Title: A GAGA principle for Motivic Zero-Cycles

Abstract: The GAGA principle says that coherent sheaves on a proper complex variety are the same as those of its analytification. Consequently, one finds that the algebraic and analytic Picard groups agree in this case. In other words, the weight-one motivic cohomology in weight one of a proper complex variety is controlled by its analytification. I will report on joint work-in-progress with Toni Annala, Tess Bouis, Elden Elmanto, Mahdi Rafiei on a mixed characteristic analogue of this story for another part of motivic cohomology: zero-cycles. We prove that motivic zero-cycles on a scheme proper and finite-type over a deeply ramified field are the same as those of its analytification.