Slopes of modular forms and reducible Galois representations: an oversight in the ghost conjecture

Slopes of modular forms and reducible Galois representations: an oversight in the ghost conjecture Pollack, Robert; Bergdall, John The ghost conjecture, formulated by this article’s authors, predicts the list of p-adic valuations of the non-zero ap-eigenvalues (“slopes”) for overconvergent p-adic modular eigenforms in terms of the Newton polygon of an easy-to-describe power series (the “ghost series”). The prediction is restricted to eigenforms whose Galois representation modulo p is reducible on a decomposition group at p. It has been discovered, however, that the conjecture is not formulated correctly. Here we explain the issue and propose a salvage.