Liu Hang
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Registered User
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Interested in algebraic geometry and algebraic K-theory.
Email:liuhang312 at gmail.com
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Mar 13 |
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Does split L-function imply split jacobian added 357 characters in body |
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Mar 13 |
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Does split L-function imply split jacobian The reduction of jacobian can split at all places with good reduction, so the local L factor splits everywhere, this is what I mean by "the L-function splits", sorry for the confusing. So could we know if the jacobian of the curve split or not from the information of the L function of the curve. More specifically, look at the genus 4 curve $C:y^3=x^6+1$, the L-function of the curve splits in the sense above, and $C$ maps to $E:y^3=x^3+1$ and $E′:y^3=x^2+1$ , so the Jacobian of $C$ splits to $E×E′×F$, how could I know if $F$ splits or not? |
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Mar 13 |
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Does split L-function imply split jacobian Thanks, Francois. But what if I only know the L function splits (not necessarily into product of L-functions, this can happen according to the reference pointed out by Felipe). |
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Mar 13 |
revised |
Does split L-function imply split jacobian added 541 characters in body |
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Mar 12 |
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Does split L-function imply split jacobian In my case, it is defined over Q or quadratic number field. |
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Mar 12 |
asked | Does split L-function imply split jacobian |
