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- W4376311920 abstract "For a split reductive group $G$ we realise identities in the Grothendieck group of $widehat{G}$-representation in terms of cycle relations between certain closed subschemes inside the affine grassmannian. These closed subschemes are obtained as a degeneration of $e$-fold products of flag varieties and, under a bound on the Hodge type, we relate the geometry of these degenerations to that of moduli spaces of $G$-valued crystalline representations of $operatorname{Gal}(overline{K}/K)$ for $K/mathbb{Q}_p$ a finite extension with ramification degree $e$. By transferring the aforementioned cycle relations to these moduli spaces we deduce one direction of the Breuil--M'ezard conjecture for $G$-valued crystalline representations with small Hodge type." @default.
- W4376311920 created "2023-05-13" @default.
- W4376311920 creator A5071724212 @default.
- W4376311920 date "2023-05-10" @default.
- W4376311920 modified "2023-09-26" @default.
- W4376311920 title "Cycles relations in the affine grassmannian and applications to Breuil--M'ezard for G-crystalline representations" @default.
- W4376311920 doi "https://doi.org/10.48550/arxiv.2305.06455" @default.
- W4376311920 hasPublicationYear "2023" @default.
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