The <Theorem of the square> states that for a line bundle $L$ on an <abelian variety> $X$ and $x,y\in X(k)$,
$$
T_{x+y}^*L\otimes L\cong T_x^*L\otimes T_y^*L.
$$

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 126 / 4 / i / Solution

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An abelian variety is a complete connected group variety. Despite its name, commutativity follows from completeness and the rigidity lemma.


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