Towards the homotopy of the K(2)-local Moore spectrum at p hsp>= hsp>2

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• 作者：Agnè ; s Beaudry ^{agnes.beaudry@colorado.edu}
• 关键词：K(2)K(2)-local ; Moore spectrum ; Morava stabilizer group
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：14 January 2017
• 年：2017
• 卷：306
• 期：Complete
• 页码：722-788
• 全文大小：999 K
• 卷排序：306

文摘

Let V(0)V(0) be the mod 2 Moore spectrum and let CC be the supersingular elliptic curve over F4F4 defined by the Weierstrass equation y2+y=x3y2+y=x3. Let FCFC be its formal group law and ECEC be the spectrum classifying the deformations of FCFC. The group of automorphisms of FCFC, which we denote by SCSC, acts on ECEC. Further, SCSC admits a surjective homomorphism to Z2Z2 whose kernel we denote by SC1. The cohomology of SC1 with coefficients in (EC)⁎V(0)(EC)⁎V(0) is the E2E2-term of a spectral sequence converging to the homotopy groups of EChSC1∧V(0), a spectrum closely related to LK(2)V(0)LK(2)V(0). In this paper, we use the algebraic duality resolution spectral sequence to compute an associated graded for H⁎(SC1;(EC)⁎V(0)). These computations rely heavily on the geometry of elliptic curves made available to us at chromatic level 2.