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October 16, 2025Open Access

Deformations of reducible Galois representations with large Selmer p-rank

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Dimensions of the p-torsion in the Bloch-Kato Selmer group can be made arbitrarily large.
The methods extend known results for small primes, paralleling Matsuno's findings.
Lifting residually reducible Galois representations allows for minimally generated Greenberg Selmer groups.
An isogenous lattice yields a Bloch-Kato Selmer group with large p-rank.

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This paper constructs Galois representations with large Selmer p-rank, highlighting implications for modular forms and existing results.

Ghate et al. (2025) studied this question.

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