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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
Affiliation:
Department of Mathematics, Imperial College, South Kensington, London SW7 2AZ, [email protected]
L. J. P. Kilford
Affiliation:
Mathematical Institute, 24–29 St Giles', Oxford OX1 3LB, [email protected]
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Abstract

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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.

Type
Research Article
Copyright
Foundation Compositio Mathematica 2005