The Coleman–Mazur eigencurve is proper at integral weights
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منابع مشابه
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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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])...
متن کاملLocal to Global Compatibility on the Eigencurve
We generalise Coleman’s construction of Hecke operators to define an action of GL2(Ql) on the space of finite slope overconvergent p-adic modular forms (l 6= p). In this way we associate to any Cp-valued point on the tame level N Coleman-Mazur eigencurve an admissible smooth representation of GL2(Ql) extending the classical construction. Using the Galois theoretic interpretation of the eigencur...
متن کاملKisin’s lectures on the eigencurve via Galois representations
1: Overview of main results. 2: The eigencurve via Galois representations. 3: Classification of crystalline Galois representations. (2 lectures). 4: Construction of potentially semi-stable deformation ring (2 lectures). 5: Modularity of potentially Barsotti-Tate representations. 6: The Fontaine-Mazur conjecture for GL2 (2 lectures). Recall the statement of the Fontaine-Mazur conjecture, which s...
متن کاملN ov 2 00 3 A counterexample to the Gouvêa – Mazur conjecture . Kevin Buzzard
Gouvêa and Mazur made a precise conjecture about slopes of modular forms. Weaker versions of this conjecture were established by Coleman and Wan. In this note, we exhibit examples contradicting the full conjecture as it currently stands. Let p be a prime number, and let N be a positive integer coprime to p. For an integer k, let fk ∈ Z[X] denote the characteristic polynomial of the Hecke operat...
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