Slope classicality in higher Coleman theory via highest weight vectors in completed cohomology.
basic_science · Level V
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- Record sourced from PubMed, PMID 36322737.
- Also identified by DOI 10.1073/pnas.2208249119 and PMC identifier 9659406.
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Abstract
We give a proof of the slope classicality theorem in classical and higher Coleman theory for modular curves of arbitrary level using the completed cohomology classes attached to overconvergent modular forms. The latter give an embedding of the quotient of overconvergent modular forms by classical modular forms, which is the obstruction space for classicality in either cohomological degree, into a unitary representation of [Formula: see text]. The <i>U<sub>p</sub></i> operator becomes a double coset, and unitarity yields slope vanishing.