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edited Jan 20 2010 at 18:26

Pete L. Clark
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edited Jan 19 2010 at 11:56

Harry Gindi
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ag.algebraic-geometry nt.number-theory arithmetic-geometry examples motivation moduli-spaces

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edited Jan 19 2010 at 11:53

norondion
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Why is one interested in the mod p reduction of modular curves and Shimura varieties?

From an article I learned that this can be used to prove the Eichler-Shimura relation which in turn proves the Hasse-Weil conjecture for modular curves. Are there similar applications for Shimura varieties?

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edited Jan 19 2010 at 11:50

Harry Gindi
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norondion
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Why is one interested in the mod p reduction of modular curves and Shimura varieties?

Why is one interested in the mod p reduction of modular curves Shimura varieties?