Abstract
We prove an equivariant Riemann–Roch formula for divisors on algebraic curves over perfect fields. By reduction to the known case of curves over algebraically closed fields, we first show a preliminary formula with coefficients in \({\mathbb{Q}}\) . We then prove and shed some further light on a divisibility result that yields a formula with integral coefficients. Moreover, we give variants of the main theorem for equivariant locally free sheaves of higher rank.
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Fischbacher-Weitz, H., Köck, B. Equivariant Riemann–Roch theorems for curves over perfect fields. manuscripta math. 128, 89–105 (2009). https://doi.org/10.1007/s00229-008-0218-3
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DOI: https://doi.org/10.1007/s00229-008-0218-3