Cohesive products of fields are constructed and their infinite Galois groups plus hyper-automorphism groups are characterized for large classes of computable Galois extensions.
[Zyw25c] David Zywina
2 Pith papers cite this work. Polarity classification is still indexing.
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For any number field K and genus g ≥ 2, there are infinitely many non-isomorphic hyperelliptic curves over K with Jacobian rank 0, 1, or 2 over K; explicit higher-rank ranges are given for small genera over Q.
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On Cohesive Products of Fields
Cohesive products of fields are constructed and their infinite Galois groups plus hyper-automorphism groups are characterized for large classes of computable Galois extensions.
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Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two
For any number field K and genus g ≥ 2, there are infinitely many non-isomorphic hyperelliptic curves over K with Jacobian rank 0, 1, or 2 over K; explicit higher-rank ranges are given for small genera over Q.