Аннотация:
The classical Weil reciprocity law is a fundamental result in the theory of algebraic curves, stating that for two meromorphic functions on a compact Riemann surface, the product of the values of one function at the divisors of the other is equal to the reciprocal product. In this talk, we explore a tropical analogue of this law.
We will begin by introducing tropical curves and tropical meromorphic functions. We then state and prove the tropical Weil reciprocity law, which takes a strikingly simple linear form. This tropical perspective not only provides a new, combinatorial viewpoint but also leads to an elegant proof of the original, classical Weil reciprocity law. The proof strategy involves decomposing the Riemann surface into simple pieces (cylinders) and observing how the relevant contributions cancel upon gluing.
Finally, we will discuss how this framework allows for the construction of a tropical Weil pairing on the group of divisors of degree zero, drawing an analogy with electrical networks and suggesting a connection to its classical counterpart. This is joint work with M. Magin.
Язык доклада: английский
Website:
https://us02web.zoom.us/j/81866745751?pwd=bEFqUUlZM1hVV0tvN0xWdXRsV2pnQT09
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