Masse
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Unregistered User
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Jan 9 |
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Do regular noetherian schemes of dimension one only have finitely many etale covers of bounded degree @pranavk. It seems that I underestimated the difficulty of this question. When you said "a zoo", it became clear to me that this question is more difficult than I had expected. As you can read in the question, I was motivated by the arithmetic and the geometric case. I was too optimistic and hoped for an easy "classification" of Dedekind schemes which would lead to a comprehensible answer. But it seems that this is too difficult. |
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Jan 8 |
asked | Does the Riemann hypothesis for liftable varieties over a finite field imply the Riemann hypothesis for all varieties over a finite field |
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Jan 8 |
awarded | ● Commentator |
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Jan 8 |
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Corresponding notion of unramified for motives (or de Rham cohomology) @Piotr. That's very useful! I didn't realize that. |
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Jan 8 |
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Corresponding notion of unramified for motives (or de Rham cohomology) @Mikhail. Thank you for your comment. |
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Jan 8 |
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Base change of semi-stable curve still semi-stable @Daniel Litt and kreck. Thank you very much. This answers my question fully. |
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Jan 8 |
revised |
Base change of semi-stable curve still semi-stable added 9 characters in body; deleted 98 characters in body |
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Jan 7 |
asked | Base change of semi-stable curve still semi-stable |
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Jan 7 |
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Do regular noetherian schemes of dimension one only have finitely many etale covers of bounded degree Your counterexample (an open affine subscheme of Spec $R$) is two-dimensional, no? Also, I'm not sure how to exclude such examples. It might be possible to do a case-by-case analysis. |
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Jan 7 |
asked | Do regular noetherian schemes of dimension one only have finitely many etale covers of bounded degree |
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Jan 5 |
asked | Corresponding notion of unramified for motives (or de Rham cohomology) |
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Jan 4 |
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On the m-th power of the Hodge bundle and Arakelov’s theorem Also, I find the condition $f_\ast omega^{\otimes n}$ non-zero in Arakelov's inequality a bit strange. Isn't the degree of the trivial line bundle zero? Thus, isn't Arakelov's inequality trivial in this case? (See for example Theorem 1.1 in the survey of Viehweg on Arakelov inequalities.) |
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Jan 4 |
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On the m-th power of the Hodge bundle and Arakelov’s theorem Thanks for your answer and sorry for the late reply! I think I'm not understanding something completely; if $f_\ast \omega^{\otimes n} =0$, it can happen that $f_\ast \omega^{\otimes (n+1)}$ is non-zero? I find this very strange...The question reuces to whether $f_\ast \omega^{\otimes n}$ is non-zero for ALL $n>>0$. (And here I really mean for ALL $n$ big enough. Thus, without exceptions.) |
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Dec 23 |
awarded | ● Editor |
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Dec 23 |
revised |
On the m-th power of the Hodge bundle and Arakelov’s theorem deleted 11 characters in body |
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Dec 23 |
asked | Does the Albanese map satisfy Torelli’s theorem |
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Dec 23 |
awarded | ● Scholar |
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Dec 23 |
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Is the moduli space of genus three smooth quartics affine? @Jason. That's what I was looking for indeed. Any nonempty effective divisor on $\mathbf P^{14}$ is ample. |
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Dec 23 |
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Is the moduli space of genus three smooth quartics affine? @Olivier. You're right. I didn't mean to say that. Rather, more generally, the moduli space of smooth hypersurfaces of degree $d$ in $N$-projective space is affine if $d>N+1$. |
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Dec 23 |
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If rational points are like entire curves, then what do algebraic points correspond to That seems reasonable. Just to convince myself a bit more. Let $X$ be curve of genus at least $two$ over a number field $K$ of big gonality. Then the set of quadratic points on $X$ is finite by Faltings-Frey. In particular, this should correspond to the fact that there are only finitely many hyperelliptic curves dominating $X$. And that of course follows from the big gonality of $X$. (Actually there are no hyp ell curves dominating $X$.) So ok, I'm convinced that this "works". |
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Dec 23 |
asked | Is the moduli space of genus three smooth quartics affine? |
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Dec 23 |
asked | If rational points are like entire curves, then what do algebraic points correspond to |
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Dec 22 |
awarded | ● Teacher |
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Dec 22 |
answered | How we obtain information about a variety from an algebraic group acting on it |
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Dec 22 |
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On the m-th power of the Hodge bundle and Arakelov’s theorem Let's say the canonical sheaf is ample. |
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Dec 21 |
awarded | ● Student |
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Dec 21 |
asked | On the m-th power of the Hodge bundle and Arakelov’s theorem |
