Compositio Mathematica· 2026Q1
Eisenstein points on the Hilbert cuspidal eigenvariety
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- Q1SCImago
- 2026year
Short summary
Researchers identified specific points on Hilbert p-adic eigenvarieties where the weight map is étale, offering new geometric insights into Hilbert automorphic forms.
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Key points
- Identified specific geometric points on Hilbert p-adic eigenvarieties at classical parallel weight 1.
- Determined all points where the weight map is étale at the intersection of cuspidal and Eisenstein loci.
- Employed a Galois theoretic approach to address difficulties with irregular pseudo-characters.
- Results offer deeper insight into the arithmetic of Hilbert automorphic forms.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract We present a comprehensive study of the geometry of Hilbert p -adic eigenvarieties at classical parallel weight 1 intersection points of their cuspidal and Eisenstein loci. For instance, we determine all such points at which the weight map is étale. The Galois theoretic approach presents genuine difficulties due to the lack of good deformation theory for pseudo-characters irregular at p and reflects the richness of the local geometry. We believe that our geometric results lead to deeper insight into the arithmetic of Hilbert automorphic forms and we produce in support several applications in Iwasawa theory.
The authors' abstract, as published at the source. Compositio Mathematica, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics