# Riemann-Roch theorem for arbitrary 1-dim schemes

Please I am looking for a reference on Riemann-Roch theorem for 1-dimensional schemes (and not necessarily varieties) if there is any.

Thank you

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Maybe you should precise what you want to be called Riemann-Roch in this context : for example, is it about divisors or line bundles ? (different things on a singular curve) –  user25309 Mar 15 '13 at 17:32
Are your schemes over a field or do you want a Riemann-Roch for $Spec(\mathbb{Z})$ and its finite covers? –  Felipe Voloch Jul 3 '13 at 7:49

## 1 Answer

You may find this paper of Hartshorne to be helpful.

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Thank you for the reference. –  user16974 Mar 15 '13 at 18:00