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The modular tower of curves over a finite field.

I want to investigate the tower of modular curves X(n)X(1) over a finite field Fq with 00Fq and pullbacks of this tower by maps CX(1).

In particular, I want to investigate the characteristic polynomial of the Frobenius on the -adic cohomology. If I knew defining equations for X(n) in terms of the parameter t on X(1), I guess I could do it but I am not sure...

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updated 2 years ago

FrédéricC gravatar image

The modular tower of curves over a finite field.

I want to investigate the tower of modular curves X(n)X(1) over a finite field Fq with 00Fq and pullbacks of this tower by maps CX(1).

In particular, I want to investigate the characteristic polynomial of the Frobenius on the -adic cohomology. If I knew defining equations for X(n) in terms of the parameter t on X(1), I guess I could do it but I am not sure...