Equivariant Riemann–Roch theorems for curves over perfect fields

Fischbacher-Weitz, Helena B.; Köck, Bernhard

doi:10.1007/s00229-008-0218-3

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Automorphism Groups Of Geometric Goppa Codes1

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2015

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“…In this section we are going to explain how Corollary 4.9 can be used to obtain permutation groups that act faithfully on geometric Goppa codes. A slightly more explicit account of the basic idea can also be found in [FW,Chapter 3].…”

Section: Automorphism Groups Of Geometric Goppa Codesmentioning

confidence: 99%

Faithfulness of Actions on Riemann-Roch Spaces

Köck¹,

Tait²

2015

Can. j. math.

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Abstract. Given a faithful action of a finite group G on an algebraic curve X of genus g X ≥ 2, we give explicit criteria for the induced action of G on the Riemann-Roch space H 0 (X, O X (D)) to be faithful, where D is a G-invariant divisor on X of degree at least 2g X − 2. This leads to a concise answer to the question when the action of G on the space H 0 (X, Ω ⊗m X ) of global holomorphic polydifferentials of order m is faithful. If X is hyperelliptic, we furthermore provide an explicit basis of H 0 (X, Ω ⊗m X ). Finally, we give applications in deformation theory and in coding theory and we discuss the analogous problem for the action of G on the first homology H 1 (X, Z/mZ) if X is a Riemann surface.

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Section: Automorphism Groups Of Geometric Goppa Codesmentioning

confidence: 99%