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NEW EXAMPLES OF p-ADICALLY RIGID AUTOMORPHIC FORMS - people brandeis

NEW EXAMPLES OF p-ADICALLY RIGID AUTOMORPHIC FORMS - people brandeis 2025

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The document presents two p-adic rigidity results for automorphic forms associated with the quasi-split unitary group U(2, 1) linked to a quadratic imaginary field. It establishes that discrete automorphic forms in cohomological degree 1 cannot be interpolated in positive-dimensional p-adic families, despite their Hodge-Tate weights being dense. This finding contrasts with the behavior of definite inner forms like U(3). Additionally, it shows that certain minimally ramified automorphic forms are rigid in a stronger sense, unable to form non-trivial families interpolating cohomological automorphic forms across any degree.

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