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arXiv · 2111.14967

Rational points on symmetric squares of constant algebraic curves over function fields

Jennifer Berg·José Felipe Voloch
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Abstract

We consider smooth projective curves C/$\mathbb{F}$ over a finite field and their symmetric squares $C^{(2)}$. For a global function field $K/\mathbb{F}$, we study the $K$-rational points of $C^{(2)}$. We describe the adelic points of $C^{(2)}$ surviving Frobenius descent and how the $K$-rational points fit there. Our methods also lead to an explicit bound on the number of $K$-rational points of $C^{(2)}$ satisfying an additional condition. Some of our results apply to arbitrary constant subvarieties of abelian varieties, however we produce examples which show that not all of our stronger conclusions extend.

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Jennifer Berg, José Felipe Voloch. 2021-11-29. Rational points on symmetric squares of constant algebraic curves over function fields. https://arxiv.org/abs/2111.14967

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