Eigenspaces of Coleman's Trace Operator

Joseph DiCapua

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arXiv · 2410.10029

Eigenspaces of Coleman's Trace Operator

Joseph DiCapua

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Abstract

The Coleman power series defined on a Lubin-Tate tower of extensions over $K$ are compatible with respect to two formal group laws: the multiplicative formal group law and some Lubin-Tate formal group law defined over $\mathcal{O}_K$. We ask if it is possible to generalize these power series in order to find power series which are compatible with respect to two Lubin-Tate formal group laws in the same way. We provide a precise formulation of this question and a partial answer towards the classification of all such power series which involves the eigenspaces of Coleman's trace operator. Some additional eigenspaces of Coleman's trace operator are also introduced.

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Joseph DiCapua. 2024-10-13. Eigenspaces of Coleman's Trace Operator. https://arxiv.org/abs/2410.10029

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