Algebraic chromatic homotopy theory for $BP_*BP$-comodules

摘要

In this paper, we study the global structure of an algebraic avatar of thederived category of ind-coherent sheaves on the moduli stack of formal groups.In analogy with the stable homotopy category, we prove a version of thenilpotence theorem as well as the chromatic convergence theorem, and constructa generalized chromatic spectral sequence. Furthermore, we discuss analogs ofthe telescope conjecture and chromatic splitting conjecture in this setting,using the local duality techniques established earlier in joint work withValenzuela.