Talk:Moduli stack of elliptic curves

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Todo

Include GIT construction (find better substitute of https://arxiv.org/pdf/1111.3032.pdf)
Arithmetic Moduli of Elliptic Curves. (AM-108) is the authoritative reference
Mumford 129-139 contains construction for all abelian varieties, special this for elliptic curves
Mumford GIT page 192 gives ${\mathcal {A}}_{1,(4,8)}$ isomorphic to $x^{4}=y^{4}+z^{4}$ minus twelve points (abelian varieties with level (4,8) structure)
Silverman also discusses weierstrauss equations over Z
https://www.math.ucla.edu/~mikehill/Research/surv-douglas2-201.pdf page 51 is an excellent reference for visualization
Weighted projective space (https://arxiv.org/pdf/1604.02441.pdf)
https://people.math.umass.edu/~tevelev/66-80.pdf and https://people.math.umass.edu/~tevelev/moduli797.pdf are excellent resources and contain more info, especially with the schotky problem

Characteristic 0

Add compactification + line bundles over compactification + modular forms as modular functions extending to the compactification

Universal elliptic curve

Page 16, show isomorphism of semidirect product as a matrix group
Then give the induced action of this new matrix group on C \times h

Construction in general / over Spec(Z)

Need Artin's criterion article to be updated.
Starting at page 59 of pdf of Deligne Rappoport gives construction using Artin's criterion - http://smtp.math.uni-bonn.de/ag/alggeom/preprints/Lesschemas.pdf
Definition of ${\mathcal {M}}$ is given on pdf page 54
scheme of curves - pdf page 18
generalized scheme of elliptic curves - pdf page 36 definition 1.12

Additional references

TOPOLOGICAL MODULAR FORMS - Paul Goerss - https://sites.math.northwestern.edu/~pgoerss/papers/Exp.1005.P.Goerss.pdf — Preceding unsigned comment added by Wundzer (talk • contribs) 18:11, 19 June 2020 (UTC)[reply]