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- W3181047887 abstract "Abstract We exhibit basic algebro-geometric results on the formal model of semi-infinite flag varieties and its Schubert varieties over an algebraically closed field ${mathbb K}$ of characteristic $neq 2$ from scratch. We show that the formal model of a semi-infinite flag variety admits a unique nice (ind-)scheme structure, its projective coordinate ring has a $mathbb {Z}$ -model and it admits a Frobenius splitting compatible with the boundaries and opposite cells in positive characteristic. This establishes the normality of the Schubert varieties of the quasi-map space with a fixed degree (instead of their limits proved in [K, Math. Ann. 371 no.2 (2018)]) when $mathsf {char}, {mathbb K} =0$ or $gg 0$ , and the higher-cohomology vanishing of their nef line bundles in arbitrary characteristic $neq 2$ . Some particular cases of these results play crucial roles in our proof [47] of a conjecture by Lam, Li, Mihalcea and Shimozono [60] that describes an isomorphism between affine and quantum K -groups of a flag manifold." @default.
- W3181047887 created "2021-07-19" @default.
- W3181047887 creator A5087446574 @default.
- W3181047887 date "2021-01-01" @default.
- W3181047887 modified "2023-09-27" @default.
- W3181047887 title "Frobenius splitting of Schubert varieties of semi-infinite flag manifolds" @default.
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- W3181047887 doi "https://doi.org/10.1017/fmp.2021.5" @default.
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