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Equivariant Riemann-Roch theorems for curves over perfect fields

Helena B. Fischbacher-Weitz·Bernhard Köck
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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 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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Helena B. Fischbacher-Weitz, Bernhard Köck. 2008-04-11. Equivariant Riemann-Roch theorems for curves over perfect fields. https://arxiv.org/abs/math/0701257

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