Abstract
We prove, in an elementary way, that a locally free sheaf of finite rank over the anisotropic real conic is the direct sum of indecomposable locally free sheaves of rank 1 or 2. Our proof is purely algebraic, and is based on a classification of graded ℂ[X, Y]-modules endowed with a certain action of the cyclic group ℤ/4ℤ.
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