Proves optimal homological vanishing line for H_i(B_n, V^{\otimes n}) giving power-saving cancellation bounds for Gauss sums and character sums over function fields, extending Patterson's conjecture.
Deligne, La conjecture de Weil
3 Pith papers cite this work, alongside 927 external citations. Polarity classification is still indexing.
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The paper proves a degree formula for Hilbert-90 quotient maps via torsion defects, classifies low-degree strata, and shows full symmetric geometric monodromy in characteristic zero.
Proves coset-refined trace theorem for cubic norm tori over finite fields with square-root cancellation bounds and analyzes nodal degeneration plus local affine branches.
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Optimal homological vanishing: cancellation of character sums and Patterson's conjecture over $\mathbb{F}_q[t]$
Proves optimal homological vanishing line for H_i(B_n, V^{\otimes n}) giving power-saving cancellation bounds for Gauss sums and character sums over function fields, extending Patterson's conjecture.
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Hilbert-90 quotient maps, torsion defects, and symmetric monodromy
The paper proves a degree formula for Hilbert-90 quotient maps via torsion defects, classifies low-degree strata, and shows full symmetric geometric monodromy in characteristic zero.
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Coset-refined trace statistics, nodal characters, and affine branches in cubic norm tori
Proves coset-refined trace theorem for cubic norm tori over finite fields with square-root cancellation bounds and analyzes nodal degeneration plus local affine branches.