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Creators/Authors contains: "Balakrishnan, Jennifer S."

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  1. ; ; ; ( , Advances in Mathematics)
    Free, publicly-accessible full text available December 1, 2024
  2. ; ; ; ( , Advances in Mathematics)
    Free, publicly-accessible full text available September 1, 2024
  3. ; ; ; ; ( , Compositio Mathematica)

    We describe how the quadratic Chabauty method may be applied to determine the set of rational points on modular curves of genus$g>1$whose Jacobians have Mordell–Weil rank$g$. This extends our previous work on the split Cartan curve of level 13 and allows us to consider modular curves that may have few known rational points or non-trivial local height contributions at primes of bad reduction. We illustrate our algorithms with a number of examples where we determine the set of rational points on several modular curves of genus 2 and 3: this includes Atkin–Lehner quotients$X_0^+(N)$of prime level$N$, the curve$X_{S_4}(13)$, as well as a few other curves relevant to Mazur's Program B. We also compute the set of rational points on the genus 6 non-split Cartan modular curve$X_{\scriptstyle \mathrm { ns}} ^+ (17)$.

     
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    Free, publicly-accessible full text available June 1, 2024
  4. ( , Snapshots of modern mathematics from Oberwolfach)
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  5. ; ; ( , La Matematica)
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  6. ; ; ; ( , Israel Journal of Mathematics)
    null (Ed.)
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  7. ; ; ( , Journal of Number Theory)
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  8. ; ( , International Mathematics Research Notices)
    Abstract We give new instances where Chabauty–Kim sets can be proved to be finite, by developing a notion of “generalised height functions” on Selmer varieties. We also explain how to compute these generalised heights in terms of iterated integrals and give the 1st explicit nonabelian Chabauty result for a curve $X/\mathbb{Q}$ whose Jacobian has Mordell–Weil rank larger than its genus. 
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  9. ; ( , Mathematics of Computation)
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  10. ( , Notices of the American Mathematical Society)
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