The 2 - adic Eigencurve is Proper
نویسندگان
چکیده
In [7], Coleman and Mazur construct a rigid analytic space E that parameterizes overconvergent and therefore classical modular eigenforms of finite slope. The geometry of E is at present poorly understood, and seems quite complicated, especially over the centre of weight space. Recently, some progress has been made in understanding the geometry of E in certain examples (see for example [3],[4]). Many questions remain. In this paper, we address the following question raised on p5 of [7]:
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The Eigencurve is Proper at Integral Weights
The eigencurve E is a rigid analytic space parameterizing overconvergent and therefore classical modular eigenforms of finite slope. Since Coleman and Mazur’s original work [10], there have been numerous generalizations [4, 6, 14], as well as alternative constructions using modular symbols [1] and p-adic representation theory [12]. In spite of these advances, several elementary questions about ...
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