A new approach to the De Rham-Witt complex
I will present a new approach to the De Rham-Witt complex inspired by the work of Antieau and Nikolaus. The approach is based on the notion of differential graded Cartier modules which are an algebraic analogue of topological Cartier modules of Antieau-Nikolaus. The linear algebra of differential graded Cartier modules is only mildly more complicated than classical F-V complexes, and the new approach allows for a more conceptual and elegant revision of classical topics such as the crystalline comparison for the De Rham-Witt complex, and some new ones, such as the relation between De Rham-Witt connections and F-gauges on a smooth characteristic p scheme.