3 papers
math.NT2025
Euler systems and relative Satake isomorphism
Li Cai, Yangyu Fan, Shilin Lai
We explain how the unramified Plancherel formula in the relative Langlands program gives a natural way of constructing test vectors which satisfy the tame norm relations of an Eule…
math.NT2025
On the Frobenius fields of abelian varieties over number fields
Ashay A. Burungale, Haruzo Hida, Shilin Lai
Let be a non-CM simple abelian variety over a number field . For a place of such that has good reduction at , let denote the Frobenius field generate…
math.NT2024
Wall crossing in Iwasawa theory
Shilin Lai
This paper sets up a framework to organize anticyclotomic Iwasawa theory in the context of the Gan-Gross-Prasad conjecture for unitary groups. We propose multiple main conjectures…