On $p$-adic Deligne--Lusztig spaces

Abstract: We discuss a new definition of $p$-adic Deligne--Lusztig spaces, as arc-sheaves on perfect algebras over the residue field. We look then at some fundamental properties of these sheaves. In particular, we show that they are ind-representable in many cases. Along the way we discuss a general result saying that the (perfect) loop space of a quasi-projective scheme over $\mathbf{Q}_p$ is an arc-sheaf.

commutative algebraalgebraic geometrynumber theory

Audience: researchers in the topic

Recent Advances in Modern p-Adic Geometry (RAMpAGe)

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