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Thursday, January 19, 2017

**Abstract:** Any one dimensional formal group law over $\mathbb{Z}_p$ is uniquely determined by the series expansion of its multiplication by $p$ map. This talk addresses the converse question: when does an endomorphism $f$ of the $p$-adic formal disk arise as the multiplication by $p$-map of a formal group? Lubin, who first studied this question, observed that if such a formal group were to exist, then $f$ would commute with an automorphism of infinite order. He formulated a conjecture under which a commuting pair of series should arise from a formal group. Using methods from p-adic Hodge theory, we prove the height one case of this conjecture.