Blueshift in chromatic homotopy theory

The chromatic perspective on stable homotopy theory organizes cohomology theories according to their height. In this talk, we briefly recall this framework, review two constructions that are known to decrease height, and explain their conjectured behaviour. We then describe an approach to these conjectures based on joint work with Heard and Valenzuela, by formulating a version of local duality in chromatic homotopy theory.