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Oct 30, 2023 at 1:28 comment added Will Sawin One can define the successive minima in this setting and give estimates in terms of the successive minima that are similar to those in the integer case, but simpler. Or one can express such a tuple and a real $r$ as a vector bundle on $\mathbb P^1_{\mathbb F_q}$ and express things in terms of the classification of vector bundles on $\mathbb P^1$. The two perspectives are equivalent and it's mainly a matter of taste.
Oct 30, 2023 at 0:59 history edited Sam Hopkins
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Oct 30, 2023 at 0:57 history asked joaopa CC BY-SA 4.0