Power Operations in Morava E-Theory of Flat Ring Spectra
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910051843702784 |
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| author | Lotenberg, Yuval |
| author_facet | Lotenberg, Yuval |
| contents | Let $E_n$ be Morava $E$-theory of height $n$. Let $R$ be a $p$-adically flat commutative ring spectrum. Then the Tate-valued Frobenius map endows $π_0 R$ with the structure of a $δ$-ring. On the other hand, we may form the $K(n)$-completed tensor product $L_{K(n)}(R \otimes E_n)$, which is a $K(n)$-local $E_n$-algebra. Then $π_0(L_{K(n)}(R \otimes E_n)) = LT_n \widehat{\otimes} π_0 R$ admits the structure of an algebra over the monad $\mathbb{T}(n)$ defined by Rezk. The $\mathbb{T}(n)$-algebra structure encodes the power operations of $L_{K(n)}(R \otimes E_n)$. In this paper we describe the $\mathbb{T}(n)$-algebra structure on $π_0(L_{K(n)}(R \otimes E_n))$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_12980 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Power Operations in Morava E-Theory of Flat Ring Spectra Lotenberg, Yuval Algebraic Topology Let $E_n$ be Morava $E$-theory of height $n$. Let $R$ be a $p$-adically flat commutative ring spectrum. Then the Tate-valued Frobenius map endows $π_0 R$ with the structure of a $δ$-ring. On the other hand, we may form the $K(n)$-completed tensor product $L_{K(n)}(R \otimes E_n)$, which is a $K(n)$-local $E_n$-algebra. Then $π_0(L_{K(n)}(R \otimes E_n)) = LT_n \widehat{\otimes} π_0 R$ admits the structure of an algebra over the monad $\mathbb{T}(n)$ defined by Rezk. The $\mathbb{T}(n)$-algebra structure encodes the power operations of $L_{K(n)}(R \otimes E_n)$. In this paper we describe the $\mathbb{T}(n)$-algebra structure on $π_0(L_{K(n)}(R \otimes E_n))$. |
| title | Power Operations in Morava E-Theory of Flat Ring Spectra |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2603.12980 |