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Structure and cohomology of moduli of fo...
Salch, Andrew...

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Structure and cohomology of moduli of formal modules by Salch, Andrew ( Author )
Lemonjar Open Access
N.A
02-05-2010
Given a commutative ring A, a "formal A-module" is a formal group equipped with an action of A. There exists a classifying ring LA of formal A-modules. This paper proves structural results about LA and about the moduli stack MfmA of formal A-modules. We use these structural results to aid in explicit calculations of flat cohomology groups of M2−budsfmA, the moduli stack of formal A-module 2-buds. For example, we find that a generator of the group H1fl(MfmZ;ω), which also generates (via the Adams-Novikov spectral sequence) the first stable homotopy group of spheres, also yields a generator of the A-module H1fl(M2−budsfmA;ω) for any torsion-free Noetherian commutative ring A. We show that the order of the A-modules H1fl(M2−budsfmA;ω) and H2fl(M2−budsfmA;ω⊗ω) are each equal to 2N1, where N1 is the leading coefficient in the 2-local zeta-function of SpecA. We also find that the cohomology of M2−budsfmA is closely connected to the delta-invariant and syzygetic ideals studied in commutative algebra: H0fl(M2−budsfmA;ω⊗ω) is the delta-invariant of the largest ideal of A which is in the kernel of every ring homomorphism A→F2, and consequently H0fl(M2−budsfmA;ω⊗ω) vanishes if and only if A is a ring in which that ideal is syzygetic.
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Article
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English
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MYR 0.00
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http://arxiv.org/abs/1005.0119
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