Regulators on some abelian coverings of P^1 \ n+2 points

par Yusuke Nemoto

jeudi 5 févr. 2026, 14:00 → 15:00 Europe/Paris

M7-411 (ENS Lyon)

The Belinson conjecture states that the special values of the L-function of a motive are related to the Beilinson regulator map. In this talk, we focus on algebraic curves. For Fermat curves, Ross constructs a K_2 element and proves that this element is non-trivial by computing the regulators explicitly, which are expressed in terms of the infinite sum of the  Beta functions.  
In this talk, we generalize Ross’s result to the generalized Fermat curve, i.e., we construct a K_2 element and express the regulators in terms of the infinite sum of multivariable hypergeometric functions, and prove that this element is non-trivial. We also give various numerical examples for the Beilinson conjecture. This is a joint work with Takuya Yamauchi.