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Jun 1, 2022 at 14:34 vote accept Monsieur Periné
May 31, 2022 at 6:15 comment added David Loeffler For the construction of Tate I referred to, see $\S9$ of these seminar notes: math.stanford.edu/~conrad/vigregroup/vigre03/moduli.pdf
May 31, 2022 at 6:03 comment added David Loeffler Oops, that was wrong, sorry. Here is a fix. There is a construction of Tate giving a moduli space for pairs $(E, P)$, over an arbitrary base scheme, such that $P$ does not have order 1, 2 or 3. Over this space the universal elliptic curve has a Weierstrass equation. So we can pull back this universal Weierstrass equation to any modular curve.
May 30, 2022 at 23:47 comment added Monsieur Periné @DavidLoeffler Is this a particular property of the Hodge bundle? I don't think it's true in general that every line bundle over an affine curve is trivial (algebraically).
May 30, 2022 at 22:26 answer added Henri Cohen timeline score: 3
May 30, 2022 at 21:09 answer added David Loeffler timeline score: 2
May 30, 2022 at 19:12 comment added David Loeffler Y(N) is affine, so the Hodge bundle is trivial automatically (modulo stackiness issues for N = 1 or 2 which mean the bundle doesn't exist)
May 30, 2022 at 16:28 history edited Monsieur Periné CC BY-SA 4.0
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S May 30, 2022 at 11:47 review First questions
May 30, 2022 at 13:56
S May 30, 2022 at 11:47 history asked Monsieur Periné CC BY-SA 4.0