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comment Non-hyperelliptic families of curves with trivial Ceresa class (or Gross-Schoen class)
My student Lalit Jain pointed out to me the paper "The Griffiths Infinitesimal Invariant for a Curve in its Jacobian," by Collino and Pirola, which shows that a family of genus-g curves whose codimension in M_g is less than ~g/3 has nontrivial Ceresa. So that's something!
Aug
22
comment Non-hyperelliptic families of curves with trivial Ceresa class (or Gross-Schoen class)
Wait so I'm completely unaware that it's "generally believed" that non-hyperelliptic curves have non-torsion Ceresa cycle -- who believes this, have they written down why they believe it, etc.?
Aug
21
comment Non-hyperelliptic families of curves with trivial Ceresa class (or Gross-Schoen class)
I just mean etale cohomology -- I suppose this is "really" a motivic question but I don't think I need to invoke anything of that kind to get at what I'm interested in.
Aug
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asked Non-hyperelliptic families of curves with trivial Ceresa class (or Gross-Schoen class)
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revised Constructing quintic number fields with certain splitting behaviour
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answered Constructing quintic number fields with certain splitting behaviour
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answered Motives over finite field not generated by hyperelliptic curves
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comment Argument for unboundedness of integral points of elliptic curves over number fields
Oh I see. But if that's what joro was asking, I don't see how his construction gives any hint of how to get unbounded rank over a fixed K.
Apr
28
comment Argument for unboundedness of integral points of elliptic curves over number fields
It should do. Just take your r points defined over disjoint quadratic fields, whose compositum is K; the MW rank over THAT field is finite, so you can certainly choose an integer x such that (sqrt(f(x))) generates a further quadratic extension of K, then you have rank r+1 and you just keep going.
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answered How many solutions to $2^a + 3^b = 2^c + 3^d$?
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answered Argument for unboundedness of integral points of elliptic curves over number fields
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