Power Operations on $K(n-1)$-Localized Morava $E$-theory at Height $n$
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917982060412928 |
|---|---|
| author | Wu, Yifan |
| author_facet | Wu, Yifan |
| contents | We calculate the $K(n-1)$-localized $E_n$ theory for symmetric groups, and deduce a modular interpretation of the total power operation $ψ^p_F$ on $F=L_{K(n-1)}E_n$ in terms of augmented deformations of formal groups and their subgroups. We compute the Dyer-Lashof algebra structure over $K(n-1)$-local $E_n$-algebra. Then we specify our calculation to the $n=2$ case. We calculate an explicit formula for $ψ^p_F$ using the formula of $ψ^p_E$, and explain connections between these computations and elliptic curves, modular forms and $p$-divisible groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07874 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Power Operations on $K(n-1)$-Localized Morava $E$-theory at Height $n$ Wu, Yifan Algebraic Topology We calculate the $K(n-1)$-localized $E_n$ theory for symmetric groups, and deduce a modular interpretation of the total power operation $ψ^p_F$ on $F=L_{K(n-1)}E_n$ in terms of augmented deformations of formal groups and their subgroups. We compute the Dyer-Lashof algebra structure over $K(n-1)$-local $E_n$-algebra. Then we specify our calculation to the $n=2$ case. We calculate an explicit formula for $ψ^p_F$ using the formula of $ψ^p_E$, and explain connections between these computations and elliptic curves, modular forms and $p$-divisible groups. |
| title | Power Operations on $K(n-1)$-Localized Morava $E$-theory at Height $n$ |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2504.07874 |