Algebraic chromatic homotopy theory for BP_∗BP-comodules

TY - JOUR

T1 - Algebraic chromatic homotopy theory for BP∗BP-comodules

AU - Barthel, Tobias

AU - Heard, Drew

PY - 2018

Y1 - 2018

N2 - In this paper, we study the global structure of an algebraic avatar of the derived category of ind-coherent sheaves on the moduli stack of formal groups. In analogy with the stable homotopy category, we prove a version of the nilpotence theorem as well as the chromatic convergence theorem, and construct a generalized chromatic spectral sequence. Furthermore, we discuss analogs of the telescope conjecture and chromatic splitting conjecture in this setting, using the local duality techniques established earlier in joint work with Valenzuela.

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

UR - http://www.scopus.com/inward/record.url?scp=85057823848&partnerID=8YFLogxK

U2 - 10.1112/plms.12158

DO - 10.1112/plms.12158

M3 - Journal article

AN - SCOPUS:85057823848

SN - 0024-6115

VL - 117

SP - 1135

EP - 1180

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

IS - 6

ER -