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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.10029 |
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| _version_ | 1866910648706793472 |
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| author | DiCapua, Joseph |
| author_facet | DiCapua, Joseph |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10029 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Eigenspaces of Coleman's Trace Operator DiCapua, Joseph Number Theory 11S 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. |
| title | Eigenspaces of Coleman's Trace Operator |
| topic | Number Theory 11S |
| url | https://arxiv.org/abs/2410.10029 |