Chabauty limits of groups of involutions in SL(2,F) for local fields

TY - JOUR

T1 - Chabauty limits of groups of involutions in SL(2,F) for local fields

AU - Ciobotaru, Corina-Gabriela

AU - Leitner, Arielle

PY - 2024

Y1 - 2024

N2 - We classify Chabauty limits of groups fixed by various (abstract) involutions over SL(2,F), where F is a finite field-extension of Q_p, with p>2. To do so, we first classify abstract involutions over SL(2,F) with F a quadratic extension of Q_p, and prove p-adic polar decompositions with respect to various subgroups of p-adic SL_2. Then we classify Chabauty limits of: Then we classify Chabauty limits of: SL(2,F) ⊂ SL(2,E), where E is a quadratic extension of F, of SL(2,R) ⊂ SL(2,C), and of H_θ⊂SL(2,F), where H_θ is the fixed point group of an F-involution θ over SL(2,F).

AB - We classify Chabauty limits of groups fixed by various (abstract) involutions over SL(2,F), where F is a finite field-extension of Q_p, with p>2. To do so, we first classify abstract involutions over SL(2,F) with F a quadratic extension of Q_p, and prove p-adic polar decompositions with respect to various subgroups of p-adic SL_2. Then we classify Chabauty limits of: Then we classify Chabauty limits of: SL(2,F) ⊂ SL(2,E), where E is a quadratic extension of F, of SL(2,R) ⊂ SL(2,C), and of H_θ⊂SL(2,F), where H_θ is the fixed point group of an F-involution θ over SL(2,F).

KW - Chabauty topology

KW - buildings

KW - groups of involutions

KW - polar decomposition

UR - http://www.scopus.com/inward/record.url?scp=85173844590&partnerID=8YFLogxK

U2 - 10.1080/00927872.2023.2262588

DO - 10.1080/00927872.2023.2262588

M3 - Journal article

SN - 0092-7872

VL - 52

SP - 1408

EP - 1431

JO - Communications in Algebra

JF - Communications in Algebra

IS - 4

ER -