The Penrose Correspondence over a Non-Archimedean Field
Abstract
Let K be a non-Archimedean local field of characteristic different from 2, and let V have dimension four over K. The Drinfeld upper half-spaces of V and Λ2V define compatible open analytic subsets of Pp(V), Gr(2,V), and Flag(1,2;V). Both restricted incidence projections are smooth and surjective. For every torsion-free discrete subgroup of PGL(V)(K), the three actions are free and properly discontinuous, and the incidence correspondence descends to smooth analytic quotients. These domains contain an explicit flag defined over an unramified extension of degree seven. A symplectic form on V equips the projective domain with a contact structure and places the Grassmannian domain in Sp4/(Sp2×Sp2). For torsion-free discrete symplectic groups, this contact structure descends to the quotient. Free discrete symplectic groups of every finite rank at least two give contact threefolds whose underlying Berkovich spaces have the homotopy type of a bouquet of circles. Every quotient of the projective domain by a torsion-free discrete group preserving the contact distribution is noncompact. For every torsion-free discrete projective linear group, the flag quotient and all fibers of its two incidence projections are noncompact; both projections are nonproper.
Related
- Multiplicity One Property for Archimedean Theta Correspondence
- Uniqueness of twisted linear periods over Archimedean division algebras
- A Mixed Robinson--Schensted--Knuth Construction in the Representation Theory of GLn over Local non-Archimedean Fields
- Generalized functions in a Non-Archimedean field
- Harmonic Norms on Quiver Representations over Non-Archimedean Fields
BibTeX
@misc{verjovsky2026penrose,
title = {{The Penrose Correspondence over a Non-Archimedean Field}},
author = {Alberto Verjovsky},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31379},
eprint = {2610.31379},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31379},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Penrose Correspondence over a Non-Archimedean Field
AU - Alberto Verjovsky
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31379
UR - https://arxiv.org/abs/2610.31379
AB - Let K be a non-Archimedean local field of characteristic different from 2, and let V have dimension four over K. The Drinfeld upper half-spaces of V and Λ^2V define compatible open analytic subsets of Pp(V), Gr(2,V), and Flag(1,2;V). Both restricted incidence projections are smooth and surjective. For every torsion-free discrete subgroup of PGL(V)(K), the three actions are free and properly discontinuous, and the incidence correspondence descends to smooth analytic quotients. These domains contain an explicit flag defined over an unramified extension of degree seven. A symplectic form on V equips the projective domain with a contact structure and places the Grassmannian domain in Sp_4/(Sp_2×Sp_2). For torsion-free discrete symplectic groups, this contact structure descends to the quotient. Free discrete symplectic groups of every finite rank at least two give contact threefolds whose underlying Berkovich spaces have the homotopy type of a bouquet of circles. Every quotient of the projective domain by a torsion-free discrete group preserving the contact distribution is noncompact. For every torsion-free discrete projective linear group, the flag quotient and all fibers of its two incidence projections are noncompact; both projections are nonproper.
ER -