On Lurie's theorem and applications
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866912192664698880 |
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| author | Davies, Jack Morgan |
| author_facet | Davies, Jack Morgan |
| contents | Lurie's theorem states that there exists a sheaf of ring spectra on the site of formally étale Deligne--Mumford stacks over the moduli stack of $p$-divisible groups of height $n$, which agrees with the classical Landweber exact functor theorem (LEFT) on affines. In other words, this theorem is a global, higher categorical refinement of the LEFT. In recent work, Lurie has introduced many of the ingredients one needs to prove this theorem, and in this article, we gather these ingredients together and prove Lurie's theorem. Applications of this theorem to Lubin--Tate theories, topological modular and automorphism forms, and Adams operations are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_00482 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On Lurie's theorem and applications Davies, Jack Morgan Algebraic Topology Algebraic Geometry 14D15, 14D23, 55P42, 55P43, 55N22 Lurie's theorem states that there exists a sheaf of ring spectra on the site of formally étale Deligne--Mumford stacks over the moduli stack of $p$-divisible groups of height $n$, which agrees with the classical Landweber exact functor theorem (LEFT) on affines. In other words, this theorem is a global, higher categorical refinement of the LEFT. In recent work, Lurie has introduced many of the ingredients one needs to prove this theorem, and in this article, we gather these ingredients together and prove Lurie's theorem. Applications of this theorem to Lubin--Tate theories, topological modular and automorphism forms, and Adams operations are also discussed. |
| title | On Lurie's theorem and applications |
| topic | Algebraic Topology Algebraic Geometry 14D15, 14D23, 55P42, 55P43, 55N22 |
| url | https://arxiv.org/abs/2007.00482 |