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.
Higher Du Bois and higher rational singularities
4 Pith papers cite this work. Polarity classification is still indexing.
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Introduces quasi-rational singularities and proves an isolated singularity is rational precisely when it is quasi-rational, Du Bois, and certain local mixed Hodge numbers vanish.
Under a codimension assumption on the singular locus, isomorphism of the m-th differential sheaf implies isomorphisms for all lower i on complex hypersurfaces, with a positive characteristic analogue discussed.
Sufficient criteria are given for ambiskew polynomial rings to be differentially smooth.
citing papers explorer
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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.
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Differential Forms and Hodge Structures on Singular Varieties
Introduces quasi-rational singularities and proves an isolated singularity is rational precisely when it is quasi-rational, Du Bois, and certain local mixed Hodge numbers vanish.
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Higher singularities for hypersurfaces
Under a codimension assumption on the singular locus, isomorphism of the m-th differential sheaf implies isomorphisms for all lower i on complex hypersurfaces, with a positive characteristic analogue discussed.
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Noncommutative differential geometry of ambiskew polynomial rings
Sufficient criteria are given for ambiskew polynomial rings to be differentially smooth.