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arXiv · 2103.02092

Anticyclotomic $\large\mu$-invariants of residually reducible Galois Representations

Debanjana Kundu·Anwesh Ray
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Abstract

Let $E$ be an elliptic curve over an imaginary quadratic field $K$, and $p$ be an odd prime such that the residual representation $E[p]$ is reducible. The $\mu$-invariant of the fine Selmer group of $E$ over the anticyclotomic $\mathbb{Z}_p$-extension of $K$ is studied. We do not impose the Heegner hypothesis on $E$, thus allowing certain primes of bad reduction to decompose infinitely in the anticyclotomic $\mathbb{Z}_p$-extension. It is shown that the fine $\mu$-invariant vanishes if certain explicit conditions are satisfied. Further, a partial converse is proven.

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Debanjana Kundu, Anwesh Ray. 2021-03-02. Anticyclotomic $\large\mu$-invariants of residually reducible Galois Representations. https://doi.org/10.1016/j.jnt.2021.06.030

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