The edge-map conjecture for integral modular forms on M0(n)\mathcal{M}_0(n)

From papers

For every positive integer nn, let TMF0(n)\operatorname{TMF}_0(n) denote the associated spectrum of topological modular forms and let MF0(n)0\operatorname{MF}_0(n)_0 denote the degree-zero modular forms for the moduli problem with level-Γ0(n)\Gamma_0(n) structure. The natural edge map

π0TMF0(n)MF0(n)0\pi_0\operatorname{TMF}_0(n)\to \operatorname{MF}_0(n)_0

is defined by the descent spectral sequence. Edge-map conjecture. For every positive integer nn, this natural edge map is an isomorphism. Such an isomorphism would allow the relevant argument to proceed without inverting gcd(6,ϕ(n))\gcd(6,\phi(n)); the source introduces it as a conjectural way to remove that localisation hypothesis, and gives no resolution.

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Sources & referencesView supporting material

Primary source

Jack Morgan Davies, “Hecke operators on topological modular forms”, arXiv:2212.06208 (2024).

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