dhy
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Member for 10 years, 6 months
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The most outrageous (or ridiculous) conjectures in mathematics
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Motivic structures on cohomology of function spaces between algebraic varieties
@JasonStarr: That might actually be the right approach for what I want; see the edits.
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Motivic structures on cohomology of function spaces between algebraic varieties
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Motivic structures on cohomology of function spaces between algebraic varieties
@YosemiteSam: I could elaborate, but it concerns a much more specialized question than the one asked here...
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Motivic structures on cohomology of function spaces between algebraic varieties
@JasonStarr: Thanks for the references! I vaguely remember you mentioning this to me at some point but couldn't recall what precisely you said. Do you mind me sending you an email with some further details?
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Uniform proof of Hasse principle for algebraic groups?
@nfdc23: Thanks! If you write that as an answer, I'll accept it (so that this question no longer shows as unanswered.)
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Collection of hypersurfaces failing to be a complete intersection
I think there should be ways to do somewhat better by projecting to a projective space so that the image becomes a hypersurface, and then doing some casework on degrees of components of this hypersurface, etc... I've never tried to do this because it seems possibly fairly ugly and I've never needed a better bound.
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Torsion $0$-cycle as difference of two points
I believe the product of two non-hyperelliptic curves should be a counterexample.
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Regarding a conjecture Fogarty proposed
Assuming that you mean the Hilbert scheme of length $n$ subschemes of projective space, this is false. See e.g. arxiv.org/abs/0803.0341. Actually, it is easy to disprove for fixed $N\geq 3$ and large enough $n$: There is a unique component $Z$ that is the closure of the locus of reduced subschemes, and it can easily be checked that the dimension of the locus of subschemes supported at a point is greater than the dimension of $Z.$