TY - UNPB

T1 - Explicit Motivic Mixed Elliptic Chabauty-Kim

AU - Corwin, David

N1 - Comments and corrections welcome!

PY - 2021/2/16

Y1 - 2021/2/16

N2 - The main point of the paper is to take the explicit motivic Chabauty-Kim method developed in papers of Dan-Cohen--Wewers and Dan-Cohen and the author and make it work for non-rational curves. In particular, we calculate the abstract form of an element of the Chabauty-Kim ideal for $\mathbb{Z}[1/\ell]$-points on a punctured elliptic curve, and lay some groundwork for certain kinds of higher genus curves. For this purpose, we develop an "explicit Tannakian Chabauty-Kim method" using $\mathbb{Q}_{p}$-Tannakian categories of Galois representations in place of $\mathbb{Q}$-linear motives. In future work, we intend to use this method to explicitly apply the Chabauty-Kim method to a curve of positive genus in a situation where Quadratic Chabauty does not apply.

AB - The main point of the paper is to take the explicit motivic Chabauty-Kim method developed in papers of Dan-Cohen--Wewers and Dan-Cohen and the author and make it work for non-rational curves. In particular, we calculate the abstract form of an element of the Chabauty-Kim ideal for $\mathbb{Z}[1/\ell]$-points on a punctured elliptic curve, and lay some groundwork for certain kinds of higher genus curves. For this purpose, we develop an "explicit Tannakian Chabauty-Kim method" using $\mathbb{Q}_{p}$-Tannakian categories of Galois representations in place of $\mathbb{Q}$-linear motives. In future work, we intend to use this method to explicitly apply the Chabauty-Kim method to a curve of positive genus in a situation where Quadratic Chabauty does not apply.

KW - math.NT

KW - math.AG

KW - 14G05 (Primary), 11F80, 19F27

M3 - פרסום מוקדם

BT - Explicit Motivic Mixed Elliptic Chabauty-Kim

ER -