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<p>The Weil reciprocity law asserts that, given two meromorphic functions <i>f</i>,&#xa0;<i>g</i> on a compact complex curve, the product of the values of <i>f</i> over the roots and poles of <i>g</i> is equal to the product of the values of <i>g</i> over the roots and poles of <i>f</i>. We state and prove a tropical version of this reciprocity; the tropical ideas lead to yet another transparent “combinatorial” proof of the classical Weil reciprocity law. Then, we construct a tropical Weil pairing on the set of divisors of degree zero.</p>

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TROPICAL WEIL’S RECIPROCITY LAW AND WEIL’S PAIRING

  • 期刊论文

  • 发表日期：

    2025年6月14日

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  • Nikita Kalinin,
  • Matthew Magin

摘要

The Weil reciprocity law asserts that, given two meromorphic functions f, g on a compact complex curve, the product of the values of f over the roots and poles of g is equal to the product of the values of g over the roots and poles of f. We state and prove a tropical version of this reciprocity; the tropical ideas lead to yet another transparent “combinatorial” proof of the classical Weil reciprocity law. Then, we construct a tropical Weil pairing on the set of divisors of degree zero.