Orateur
Description
Bertrand and Gabriele introduced to the world a derived algebraic geometry way of thinking about coefficients for cohomology theories, starting with their treatment of chern characters, mixed graded complexes and sheaves on the loop space. Taking inspiration from this story, I want to present a way to describe the deformation theory of motivic cohomology and algebraic cycles using a non-representable version of Dieudonné theory which, in positive and mixed characteristics, takes as input prismatic F-gauges and produces modules over (a version of) the Raynaud ring; this was first understood by Ekedahl and later revisited by Jacob Lurie and Yuanning Zhang. Our main results generalize Bloch and Stienstra's calculation of the deformation functor of algebraic cycles and is a motivic refinement of McCandless' work on cyclotomic spectra and Cartier modules.
This is joint work in progress with Shubhodip Mondal.