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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… Click to show full 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 GL2(ℚp). The Up operator becomes a double coset, and unitarity yields slope vanishing.
Keywords:
coleman theory;
slope classicality;
classicality;
completed cohomology;
higher coleman
Journal Title: Proceedings of the National Academy of Sciences of the United States of America
Year Published: 2022
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Journal Title: Proceedings of the National Academy of Sciences of the United States of America
Year Published: 2022
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!