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The 2-adic eigencurve at the boundary of weight space

Published online by Cambridge University Press:  21 April 2005

Kevin Buzzard
Department of Mathematics, Imperial College, South Kensington, London SW7 2AZ,
L. J. P. Kilford
Mathematical Institute, 24–29 St Giles', Oxford OX1 3LB,
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We prove that, near the boundary of weight space, the 2-adic eigencurve of tame level 1 can be written as an infinite disjoint union of ‘evenly spaced’ annuli, and on each annulus the slopes of the corresponding overconvergent eigenforms tend to zero.

Research Article
Foundation Compositio Mathematica 2005