Iwasawa invariants of finite spectra
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914900227391488 |
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| author | Maison, Austin Salch, Andrew |
| author_facet | Maison, Austin Salch, Andrew |
| contents | We calculate the classical Iwasawa invariants of the Iwasawa modules associated to the $p$-adic topological $K$-theory of finite spectra. We show that the graded average of the orders of $n$ consecutive $K(1)$-local homotopy groups of a finite spectrum $X$ grows asymptotically like $\frac{-\log_p(n)}{2}$ times the total Iwasawa $λ$-invariant of $X$. We show that the Iwasawa $μ$-invariants of finite spectra are all zero. Finally, we prove a spectral analogue of a weak form of the Iwasawa Main Conjecture, describing the orders of the $K(1)$-local homotopy groups of a certain ``torsion-free replacement'' of $X$ in terms of the characteristic polynomials of the Iwasawa modules associated to $X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02163 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Iwasawa invariants of finite spectra Maison, Austin Salch, Andrew Algebraic Topology Number Theory We calculate the classical Iwasawa invariants of the Iwasawa modules associated to the $p$-adic topological $K$-theory of finite spectra. We show that the graded average of the orders of $n$ consecutive $K(1)$-local homotopy groups of a finite spectrum $X$ grows asymptotically like $\frac{-\log_p(n)}{2}$ times the total Iwasawa $λ$-invariant of $X$. We show that the Iwasawa $μ$-invariants of finite spectra are all zero. Finally, we prove a spectral analogue of a weak form of the Iwasawa Main Conjecture, describing the orders of the $K(1)$-local homotopy groups of a certain ``torsion-free replacement'' of $X$ in terms of the characteristic polynomials of the Iwasawa modules associated to $X$. |
| title | Iwasawa invariants of finite spectra |
| topic | Algebraic Topology Number Theory |
| url | https://arxiv.org/abs/2408.02163 |