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Mar 2, 2011 at 2:33 comment added JSE Not sure whether you can achieve any possible local monodromy with Jacobians.
Mar 1, 2011 at 7:50 comment added S. Carnahan Sorry for not replying. I'm afraid I am still trying to digest what the level structure argument says in the case of a genus 1 family. At any rate, for the local construction you just added, can you choose those abelian varieties to be Jacobians?
Mar 1, 2011 at 2:10 history edited JSE CC BY-SA 2.5
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Feb 28, 2011 at 20:31 history answered JSE CC BY-SA 2.5