Infinite families of graph manifolds and Seifert fibered spaces contain essential tori that are not detected by any ideal point of the SL2-character variety over any algebraically closed field.
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Essential tori in 3-manifolds not detected in any characteristic
Infinite families of graph manifolds and Seifert fibered spaces contain essential tori that are not detected by any ideal point of the SL2-character variety over any algebraically closed field.