p-Adic Geometry and Homotopy Theory
The aim of the conference is to develop the current interplay between arithmetic algebraic geometry and stable homotopy theory. Using structured ring spectra one can form topological structure sheaves for moduli stacks of elliptic curves or other abelian varieties, whose ring spectra of global sections define powerful new homology theories. Using sheaves of infinity-categories one can form topological crystalline cohomology, with associated de Rham-Witt complexes closely related to topological cyclic homology and p-adic algebraic K-theory. For complete local rings of mixed characteristic, or for structured ring spectra of mixed chromatic types, there are log (= logarithmic) geometric extensions of these theories, leading to de Rham-Witt complexes with log poles, log topological cyclic homology and log K-theory. The hope is that both algebraic geometers and homotopy theorists will have something to learn from the modern developments in these adjacent fields.