Algebraic loop groups and moduli spaces of bundles

By G. Faltings. 2003

193 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/feb634dd5fd7ca5bc6b4e10e826999c52210c829

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Citations in the corpus

The spherical Hecke algebra for affine Kac-Moody groups I (2008, methodology): “In principle, in what follows we could work with arbitrary Q using the construction of [5].”
Local models in the ramified case, II: Splitting models (2002, background): “dentiﬁed with Schubert varieties in the aﬃne Grassmannian; therefore the inverse images under the smooth morphisms πit are also (reduced) Schubert varieties in the aﬃne ﬂag variety. By [G1] (see also [F1]) all Schubert varieties in the aﬃne ﬂag variety are normal, simultaneously Frobenius split, and”
Local models of Shimura varieties and a conjecture of Kottwitz (2011, methodology): “The main ingredients in the proof of this theorem are results of [16, 47] on the structure of Schubert varieties in affine flag varieties and the coherence conjecture of [47] which was shown by the second-named author in [74].”
Le lemme fondamental pour les algebres de Lie (2008, background): “D’après [4] et [21], on sait que Gv est strictement représentable par un ind-schéma sur k.”
On the coherence conjecture of Pappas and Rapoport (2010, background): “rminant of the cohomology detRΓ(P1,adE)−1. Therefore ω−1 BunG is isomorphic to the pullback along BunG →BunGL(LieG) of the inverse of the determinant of cohomology line bundle. As is well-known (e.g. [Fa]), the pullback of the latter line bundle on BunGL(V) to GrGL(V) is the determinant line bundle ”
Ekedahl–Oort and Newton strata for Shimura varieties of PEL type (2010, background): “ a ﬁeld kand a linear algebraic group Hwe denote by LHthe loop group. It is the group ind-scheme over krepresenting the sheaf for the fpqc-topology (k-algebras) → (groups), R→ LH(R) := H(R((z))), see [Fal] Deﬁnition 1. We denote by LGthe loop group of GFp. 28 Recall that µ∈ X∗(T) is the dominant cow”
Uniformization of $${\mathcal {G}}$$-bundles (2007, methodology): “In the case of constant group schemes this was used to reduce to problems for tori e.g., Faltings used this result to construct line bundles of central charge one on BunG (see [ 13 ]).”
Projectivity of the Witt vector affine Grassmannian (2015, background): “e 2h∨-th power of LG, where h∨ is the dual Coxeter number. E.g., if G = E8, the primitive line bundle should be a 60-th root of the line bundle coming from the adjoint representation of E8. Faltings, [Fal03], constructed the primitive line bundle by constructing natural divisors (on the correspondin”
Twisted loop groups and their affine flag varieties (2006, background): “Important results on the structure of algebraic loop groups and their associated flag varieties are due to Beauville, Laszlo, Sorger, Faltings, Beilinson, Drinfeld and Gaitsgory, cf. [B-L], [BLS], [L-S], [ Fa1 ], [B-D], [G].”
The minimal degeneration singularities in the affine Grassmannians (2003, unknown): “Since (LG · λ)∩Gμ is a transverse slice to Gλ, and Gμ is a normal variety [10, 16, 7, 13], the variety (LG · λ) ∩ Gμ is also normal and irreducible.”
Kloosterman sheaves for reductive groups (2010, unknown): “If G = G×P1 is a split group, a proof of this result can be found in [14] or [24].”
The Newton stratification on deformations of local G-shtukas (2008, background): “1, for SLn or [12], Theorem 8 and Remark before Corollary 11, in general) this local ring is a normal integral domain and Cohen–Macaulay.”