What question did this study set out to answer?

The aim is to establish a central-image criterion relating Selmer inclusion certificates and reduced central images.

June 1, 2026Open Access

Central Image from Local Selmer Inclusion Certificates

Key Points

The aim is to establish a central-image criterion relating Selmer inclusion certificates and reduced central images.
Proves the central-image criterion using two unreduced Selmer inclusion certificates.
Identifies the structural elements needed from the previous core of the TEBAC BSD program.
Focuses on local spectral-to-Kummer response identities as the remaining challenge.
Establishes that the reduced central image equality holds under specified conditions.
Does not provide a standalone proof of the Birch-Swinnerton-Dyer conjecture but defines the subsequent arithmetic tasks.

Abstract

This preprint is Core II of the TEBAC BSD program. It proves a claim-safe central-image criterion: two unreduced Selmer inclusion certificates imply the reduced central image equality \ (E (K₄, ₐ) =E (M₄, ₐ) S^red₄, ₂₄₍\). The module does not claim a standalone proof of the Birch--Swinnerton--Dyer conjecture. It supplies the structural bridge needed after Core I and identifies the remaining arithmetic burden as the construction of local spectral-to-Kummer response identities.

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Cite This Study

Tosho Lazarov Karadzhov (Sat,) studied this question.

synapsesocial.com/papers/6a1d234302fbce9130638da8 https://doi.org/https://doi.org/10.5281/zenodo.20466355

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