Continuous semisimple geometric representations π₁(X,D)→GL_n(F) (char p) are finite in number for curves with arbitrary D and for tame D=0 in any dimension when p is odd, and for liftable representations for any p.
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3 Pith papers cite this work, alongside 207 external citations. Polarity classification is still indexing.
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Under standard Taylor-Wiles hypotheses, every irreducible 2-dimensional totally odd mod p Galois representation of the absolute Galois group of a totally real field F admits lifts on arbitrary prescribed components of local deformation rings, allowing potentially semistable conditions with arbitrary
For n greater than or equal to 3 and sufficiently generic weights, the universal supersingular representation of GL_n(k) is non-admissible and of infinite length.
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On the Finiteness of Geometric Representations for Varieties over Finite Fields
Continuous semisimple geometric representations π₁(X,D)→GL_n(F) (char p) are finite in number for curves with arbitrary D and for tame D=0 in any dimension when p is odd, and for liftable representations for any p.
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Prescribed lifts of 2-dimensional representations
Under standard Taylor-Wiles hypotheses, every irreducible 2-dimensional totally odd mod p Galois representation of the absolute Galois group of a totally real field F admits lifts on arbitrary prescribed components of local deformation rings, allowing potentially semistable conditions with arbitrary
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Non-admissibility of some universal supersingular representations
For n greater than or equal to 3 and sufficiently generic weights, the universal supersingular representation of GL_n(k) is non-admissible and of infinite length.