The Halo Conjecture for GL2
Hansheng Diao, Zijian Yao
TL;DR
This paper proves the Halo conjecture concerning the geometric structure of the eigencurve over the boundary of the weight space, confirming long-standing predictions by Coleman-Mazur and Buzzard-Kilford.
Contribution
It provides a rigorous proof of the Halo conjecture for GL2, advancing understanding of eigencurve geometry in number theory.
Findings
Confirmed the Halo conjecture for GL2 eigencurves
Described the geometric structure over the boundary of the weight space
Validated predictions by Coleman-Mazur and Buzzard-Kilford
Abstract
We prove the Halo conjecture on the geometry of the eigencurve over the boundary of the weight space, predicted by Coleman-Mazur and Buzzard-Kilford.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Finite Group Theory Research · Algebraic Geometry and Number Theory