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.
Ring objects in the equivariant de- rived Satake category arising from Coulomb branches
9 Pith papers cite this work, alongside 628 external citations. Polarity classification is still indexing.
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The coordinate ring of the universal centralizer equals the result of applying Demazure operators to the coordinate ring of X precisely when the W-fixed points of the Weil restriction of X is an integral scheme.
The condensed fundamental group of Spec(Z) is non-trivial, hence Spec(Z) is not condensed contractible.
For the standard representation of Sp_{2n}(C), the Gaiotto locus is the Bialynicki-Birula closure associated to U(Sp_{2n-2}(C)) inside the nilpotent cone, and its intersection with the stable cotangent chart is the closure of the conormal bundle to the one-spinor stratum of the generalized theta-div
The nth Amitsur group is a stable G-birational invariant of smooth projective G-varieties over char-0 fields for all n≥2.
Lang-Trotter conjecture for elliptic curve pairs implies new Zilber-Pink cases for curves in A_3 via André's G-functions method, without boundary intersection assumptions.
A new fibration theorem implies solvable descent, solving the Grunwald problem for solvable groups up to the Brauer-Manin obstruction.
Shape theory for condensed anima recovers classical shape for paracompact compactly generated and locally contractible spaces while extending sheaf-condensed cohomology comparisons.
Two Zilber-Pink-type statements are proved in Y(1)^n assuming a weak Lang-Trotter conjecture for pairs of elliptic curves.
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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The coordinate ring of the universal centralizer via Demazure operators
The coordinate ring of the universal centralizer equals the result of applying Demazure operators to the coordinate ring of X precisely when the W-fixed points of the Weil restriction of X is an integral scheme.
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On Galois categories and condensed contractible schemes
The condensed fundamental group of Spec(Z) is non-trivial, hence Spec(Z) is not condensed contractible.
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Gaiotto Loci and the Nilpotent Cone for $\mathrm{Sp}_{2n}(\mathbb C)$
For the standard representation of Sp_{2n}(C), the Gaiotto locus is the Bialynicki-Birula closure associated to U(Sp_{2n-2}(C)) inside the nilpotent cone, and its intersection with the stable cotangent chart is the closure of the conormal bundle to the one-spinor stratum of the generalized theta-div
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Birational invariance of higher Amitsur groups
The nth Amitsur group is a stable G-birational invariant of smooth projective G-varieties over char-0 fields for all n≥2.
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Lang-Trotter phenomena and unlikely intersections
Lang-Trotter conjecture for elliptic curve pairs implies new Zilber-Pink cases for curves in A_3 via André's G-functions method, without boundary intersection assumptions.
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Solvable Descent and the Grunwald Problem for Solvable Groups
A new fibration theorem implies solvable descent, solving the Grunwald problem for solvable groups up to the Brauer-Manin obstruction.
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Shape theory for condensed anima
Shape theory for condensed anima recovers classical shape for paracompact compactly generated and locally contractible spaces while extending sheaf-condensed cohomology comparisons.
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A note on Zilber-Pink in $Y(1)^n$
Two Zilber-Pink-type statements are proved in Y(1)^n assuming a weak Lang-Trotter conjecture for pairs of elliptic curves.