Timeline for Generalization of torsion points on Jacobian of genus 2 over finite fields (with respect to the theta divisor)
Current License: CC BY-SA 4.0
7 events
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| Jun 23, 2021 at 13:18 | history | edited | Jef | CC BY-SA 4.0 |
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| May 15, 2021 at 15:43 | comment | added | Jef | It's not obvious, and is specific to the theory of curves and jacobian varieties. You can look at Milne's notes on abelian varieties, Chapter III, Section 9 ('Obtaining coverings of a curve from its Jacobian') | |
| May 15, 2021 at 13:48 | comment | added | AVP82000 | It is still unclear to me why the preimage of C under [n] would be smooth and irreducible. I tried looking it up but was unsuccessful. I have a feeling that Prop A.3.2.4 from Diophantine Geometry by Hindry and Silverman, which says if $f : X \rightarrow Y$ is a finite morphism between 2 projective varities, if $D$ is an ample divisor on $Y$, then $f^* D$ is an ample divisor on $X$ maybe useful, but I don't understand it very well, so maybe it is completly wrong? | |
| May 5, 2021 at 19:43 | comment | added | AVP82000 | Thanks a lot for this answer, it already helps me a lot, I am not very well-versed in Algebraic geometry, but I am taking my time to understand your answer to the first question. For references for the answer to the second question, I found the Chapter in Diophantine Geometry by Hindry and Silverman useful, it has all the theorems used. | |
| May 5, 2021 at 16:27 | vote | accept | AVP82000 | ||
| May 5, 2021 at 9:03 | history | edited | Jef | CC BY-SA 4.0 |
edited body
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| May 5, 2021 at 8:56 | history | answered | Jef | CC BY-SA 4.0 |