Frobenius Quantales, Serre Quantales and the Riemann–Roch Theorem

Studia Logica 110 (2):405-427 (2021)
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Abstract

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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Quantales and (noncommutative) linear logic.David N. Yetter - 1990 - Journal of Symbolic Logic 55 (1):41-64.

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