4 papers
Murmurations, Periods, and Local Factors
Dane Wachs
We prove that over function fields F_q(t), the Tate-Shafarevich group |Sha| is an invariant of the cyclotomic type of the L-polynomial, so that |Sha|-stratified murmuration densiti…
Murmurations of Elliptic Curves over Function Fields
Dane Wachs
We compute the first murmurations for elliptic curves over function fields F_q(t): oscillatory patterns in average Frobenius traces that separate rank-0 from rank-1 curves, with z-…
BSD Invariants and Murmurations of Elliptic Curves
Dane Wachs
We investigate the interaction between Birch and Swinnerton-Dyer (BSD) invariants and the murmuration phenomenon for elliptic curves over the rational numbers. Our study, based on…
The Derived Adelic Cohomology Conjecture for Elliptic Curves
Dane Wachs
We propose a novel derived cohomological framework for the Birch and Swinnerton-Dyer (BSD) conjecture for elliptic curves. In our approach, local arithmetic data are encoded in der…