Algebraic chromatic homotopy theory for BP∗BP-comodules
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Algebraic chromatic homotopy theory for BP∗BP-comodules. / Barthel, Tobias; Heard, Drew.
In: Proceedings of the London Mathematical Society, Vol. 117, No. 6, 2018, p. 1135-1180.Research output: Contribution to journal › Journal article › Research › peer-review
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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
VL - 117
SP - 1135
EP - 1180
JO - Proceedings of the London Mathematical Society
JF - Proceedings of the London Mathematical Society
SN - 0024-6115
IS - 6
ER -
ID: 211105618