Proves finiteness of continuous semisimple geometric representations to GL_n(F) for curves with arbitrary D, varieties with D=0, and liftable representations.
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For primes N and p with N ≡ 1 mod p, the rank r of Mazur's Eisenstein Hecke algebra equals one plus the vanishing order of a mod-p zeta element interpolating L-values at -1 when r is 2 or 3, with a uniform extension to level N² and partial results for higher ranks.
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On the Finiteness of Geometric Representations for Varieties over Finite Fields
Proves finiteness of continuous semisimple geometric representations to GL_n(F) for curves with arbitrary D, varieties with D=0, and liftable representations.
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A new perspective on the rank of Mazur's Eisenstein Hecke algebra
For primes N and p with N ≡ 1 mod p, the rank r of Mazur's Eisenstein Hecke algebra equals one plus the vanishing order of a mod-p zeta element interpolating L-values at -1 when r is 2 or 3, with a uniform extension to level N² and partial results for higher ranks.