Studia Logica 110 (2):405-427 (2022)

The Riemann–Roch theorem for algebraic curves is derived from a theorem for Girard quantales. Serre duality is shown to be a quantalic phenomenon. An example provides a Girard quantale satisfying the Riemann–Roch theorem, where the associated curve is non-connected and irreducible.
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DOI 10.1007/s11225-021-09970-1
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Quantales and (Noncommutative) Linear Logic.David N. Yetter - 1990 - Journal of Symbolic Logic 55 (1):41-64.

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