Talk:Moduli stack of elliptic curves

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)