TY - JOUR

T1 - Tropical Weil's reciprocity law and Weil's pairing

AU - Kalinin, Nikita

AU - Магин, Матвей Ильич

PY - 2025/6/14

Y1 - 2025/6/14

N2 - 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.

AB - 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.

KW - Tropical curve

KW - Weil’s pairing

KW - Weil’s reciprocity law

UR - https://link.springer.com/article/10.1007/s10958-025-07754-9

UR - https://www.mendeley.com/catalogue/592fa739-2242-36a2-8343-05840e6fcde5/

U2 - 10.1007/s10958-025-07754-9

DO - 10.1007/s10958-025-07754-9

M3 - Article

JO - Journal of Mathematical Sciences (Switzerland)

JF - Journal of Mathematical Sciences (Switzerland)

SN - 1072-3374

ER -