Overview

This collaboration brings together mathematicians from a range of algebraic fields to study new ideas which have emerged over the last two decades in mixed characteristic algebraic geometry.  These new ideas, which we broadly capture with the term “perfection”, include prismatic cohomology, perfectoid spaces, and the Cartier-Witt stack.  Current work in the area also incorporates a wide variety of techniques from related fields including systematic use of derived algebraic geometry and \(K\)-theory.  With this in mind the collaboration team has been assembled to cover a broad range of mathematics to tackle major open questions in number theory, algebraic geometry, \(p\)-adic geometry, commutative algebra, and algebraic topology.