Chabauty limits of diagonal Cartan subgroups of SL(n,Qp)

2021 ◽  
Author(s):  
Corina Ciobotaru ◽  
Arielle Leitner ◽  
Alain Valette
Keyword(s):  
Cartan Subgroups

scholarly journals Modular forms invariant under non-split Cartan subgroups

2020 ◽  
Vol 89 (324) ◽  
pp. 1969-1991
Author(s):  
Pietro Mercuri ◽  
René Schoof
Keyword(s):  
Modular Forms ◽  
Cartan Subgroups

Cartan Subgroups and Lattices in Semi-Simple Groups

1972 ◽  
Vol 96 (2) ◽  
pp. 296 ◽  
Author(s):  
Gopal Prasad ◽  
M. S. Raghunathan
Keyword(s):  
Simple Groups ◽  
Cartan Subgroups

Actions of Cartan subgroups

1995 ◽  
Vol 90 (1-3) ◽  
pp. 253-294 ◽  
Author(s):  
Shahar Mozes
Keyword(s):  
Cartan Subgroups

scholarly journals A MODULI INTERPRETATION FOR THE NON-SPLIT CARTAN MODULAR CURVE

2017 ◽  
Vol 60 (2) ◽  
pp. 411-434 ◽  
Author(s):  
MARUSIA REBOLLEDO ◽  
CHRISTIAN WUTHRICH
Keyword(s):  
Elliptic Curves ◽  
Half Plane ◽  
London Math ◽  
Number Fields ◽  
Arithmetic Geometry ◽  
Modular Curves ◽  
Torsion Points ◽  
Modular Curve ◽  
Upper Half Plane ◽  
Cartan Subgroups

AbstractModular curves likeX0(N) andX1(N) appear very frequently in arithmetic geometry. While their complex points are obtained as a quotient of the upper half plane by some subgroups of SL2(ℤ), they allow for a more arithmetic description as a solution to a moduli problem. We wish to give such a moduli description for two other modular curves, denoted here byXnsp(p) andXnsp+(p) associated to non-split Cartan subgroups and their normaliser in GL2(𝔽p). These modular curves appear for instance in Serre's problem of classifying all possible Galois structures ofp-torsion points on elliptic curves over number fields. We give then a moduli-theoretic interpretation and a new proof of a result of Chen (Proc. London Math. Soc.(3)77(1) (1998), 1–38;J. Algebra231(1) (2000), 414–448).

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