Tags: #todo #MOC #algebraic_geometry #number_theory
supersingular elliptic curves: ?
Relation to Birch and Swinnerton-Dyer conjecture Pasted image 20211106013954.png❗ Pasted image 20211106014015.png❗ Pasted image 20211106014643.png❗
Hasse bounds Pasted image 20211106014716.png❗
Jonathan Love! Shows some cool consequences of the Beilinson Bloch conjecture, primarily a 2-parameter family of elliptic curve where the image \({\operatorname{CH}}^1(E_1)_0 \otimes{\operatorname{CH}}^1(E_2)_0 \to {\operatorname{CH}}^2(E_1 \times E_2)\) is finite. BB predicts this is always finite when defined over \(k\) a number field.
Start with the category of elliptic curves : should be pointed algebraic group, so a [[slice category|coslice category]] over a terminal object..?
An elliptic curve \(E\) over a scheme \(S\) is a smooth proper morphism \(f:E\to S\) with a section such that the closed fibers of \(f\) are genus 1 curves.