Nearby Cycles for Local Models of Some Shimura Varieties

Compositio Mathematica, 2001

63 citations recorded by the source corpus.

Kottwitz conjectured a formula for the (semi-simple) trace of Frobenius on the nearby cycles for the local model of a Shimura variety with Iwahori-type level structure. In this paper, we prove his conjecture in the linear and symplectic cases by adapting an argument of Gaitsgory, who proved an analogous theorem in the equal characteristic case.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/efddb02075b997e467ea554f97eabfae90e30860

Citations in the corpus

• Local models of Shimura varieties, I. Geometry and combinatorics (2010, unknown): “Then in (i), we have Admf ({µ}) = Permf ({µ}) for any {µ} and any f when R involves only type A; this was proved in the case of minuscule {µ} in [KR, 9.6], and the general case is an immediate consequence of Görtz’s result [Gö4, Cor. 9] (which itself makes crucial use of the cited result in the Iw”
• Integral models of Shimura varieties with parahoric level structure (2015, unknown): “We refer the reader to [31], [33], [36], for more details, additional references and background on nearby cycles of integral models of Shimura varieties.”
• Local models in the ramified case. III Unitary groups (2007, unknown): “When the group G is of type A or C and is split over Qp, Haines and Ngo [ HN ] have calculated the semi-simple trace of Frobenius on the sheaves of nearby cycles at any point in the reduction of the natural model at any prime ideal of OE of residue characteristic p. Indeed, they give a group-theoret”
• Alcoves associated to special fibers of local models (2001, unknown): “This set parametrizes the strata in the special fiber of the local model considered in [8], since the definition thereof uses the standard representation of the symplectic group.”
• Local models of Shimura varieties and a conjecture of Kottwitz (2011, unknown): “In the split Iwahori case, as a corollary of this theorem, one can give an explicit formula for the semi-simple Frobenius trace function using Bernstein’s presentation of the Iwahori-Hecke algebra, as was explained in [25].”