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• W3100775660 abstract "We study the variation of $unicode[STIX]{x1D707}$ -invariants in Hida families with residually reducible Galois representations. We prove a lower bound for these invariants which is often expressible in terms of the $p$ -adic zeta function. This lower bound forces these $unicode[STIX]{x1D707}$ -invariants to be unbounded along the family, and we conjecture that this lower bound is an equality. When $U_{p}-1$ generates the cuspidal Eisenstein ideal, we establish this conjecture and further prove that the $p$ -adic $L$ -function is simply a power of $p$ up to a unit (i.e. $unicode[STIX]{x1D706}=0$ ). On the algebraic side, we prove analogous statements for the associated Selmer groups which, in particular, establishes the main conjecture for such forms." @default.
• W3100775660 created "2020-11-23" @default.
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• W3100775660 date "2019-04-10" @default.
• W3100775660 modified "2023-09-30" @default.
• W3100775660 title "Congruences with Eisenstein series and -invariants" @default.
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• W3100775660 doi "https://doi.org/10.1112/s0010437x19007127" @default.
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