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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2$\begingroup$ 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) $\endgroup$– user25309Commented Mar 15, 2013 at 17:32
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2$\begingroup$ Are your schemes over a field or do you want a Riemann-Roch for $Spec(\mathbb{Z})$ and its finite covers? $\endgroup$– Felipe VolochCommented Jul 3, 2013 at 7:49
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$\begingroup$ There is also arithmetic Rieman-Roch for prime spectrum of ring of integers of number field. Like here uio.no/studier/emner/matnat/math/MAT4250/h18/arithmeticrr.pdf $\endgroup$– Galois groupCommented Oct 15, 2023 at 20:25
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1 Answer
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You may find the paper Generalized divisors on Gorenstein curves and a theorem of Noether of Hartshorne to be helpful.
answered Mar 15, 2013 at 17:53