Moduli stack of oriented formal groups and cellular motivic spectra over $\mathbf C$
| Autor: | Gregoric, Rok |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We exhibit a relationship between motivic homotopy theory and spectral algebraic geometry, based on the motivic $\tau$-deformation picture of Gheorghe, Isaksen, Wang, Xu. More precisely, we identify cellular motivic spectra over $\mathbf C$ with ind-coherent sheaves (in a slightly non-standard sense) on a certain spectral stack $\tau_{\ge 0}(\mathcal M_\mathrm{FG}^\mathrm{or})$. The latter is the connective cover of the non-connective spectral stack $\mathcal M_\mathrm{FG}^\mathrm{or}$, the moduli stack of oriented formal groups, which we have introduced previously and studied in connection with chromatic homotopy theory. We also provide a geometric origin on the level of stacks for the observed $\tau$-deformation behavior on the level of sheaves, based on a notion of extended effective Cartier divisors in spectral algebraic geometry. Comment: 26 pages. Fixed glaring typo in the abstract |
| Databáze: | arXiv |
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