On the geometric connected components of moduli spaces of p-adic shtukas and local Shimura varieties

2021/07/08 by Gleason, Ian · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2107.03579

Abstract

We study topological properties of moduli spaces of p-adic shtukas and local Shimura varieties. On one hand, we construct and study the specialization map for moduli spaces of p-adic shtukas at parahoric level whose target is an affine Deligne-Lusztig variety. On the other hand, given a p-adic shtuka datum (G, b, μ), with G unramified over ℚ_p and such that (b, μ) is HN-irreducible, we determine the set of geometric connected components of infinite level moduli spaces of p-adic shtukas. In other words, we understand π₀(Sht_(G,b,μ,∞) × Spd ℂ_p) with its right G(ℚ_p) × G_b (ℚp ) × W_E -action. As a corollary, we prove new cases of a conjecture of Rapoport and Viehmann.

Cited by

• Towards a p-adic nowhere density conjecture of Hecke Orbits

Related

• Moduli spaces of local G-shtukas
• p-adic shtukas and the theory of global and local Shimura varieties
• S=T for Shimura Varieties and Moduli Spaces of p-adic Shtukas
• The connected components of affine Deligne–Lusztig varieties
• p-adic Borel extension for local Shimura varieties