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Computing the semistable reduction of a particular plane quartic curve at $p=3$

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arxiv 2305.00288 v1 pith:JNVHAOLF submitted 2023-04-29 math.NT math.AG

Ole Ossen This is my paper · ORCID
classification math.NTmath.AG
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abstract

We explain how to determine the semistable reduction of a particular plane quartic curve at $p=3$ that appears in the attempts of Rouse, Sutherland, and Zureick-Brown to compute the rational points on the non-split Cartan modular curve $X^+_{ns}(27)$.

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  1. Rational points on the non-split Cartan modular curve of level 27 and quadratic Chabauty over number fields

    math.NT 2025-01 conditional novelty 7.0 of 10

    The normalizer of the non-split Cartan subgroup of level 27 does not occur as a 3-adic Galois image of a non-CM elliptic curve over Q, completing the 3-adic classification.

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