WebThe eigencurve is an honest moduli space---it parametrises families of finite slope overconvergent modular eigenforms (or more precisely, of systems of overconvergent finite slope Hecke eigenvalues)---but I know of no "natural" properties of p-adic modular forms that one can deduce from any geometric structure, other than e.g. the consequences of the … WebAug 12, 2024 · Let us recall [53, page 236] that it is the proper flat scheme of relative dimension 1 over \(\mathbb {Z}\) (or algebraic stack in the case N ≤ 2) representing the functor which to a scheme S attaches the set of isomorphism classes of triplets (E, H, α), where E is a generalized elliptic curve Footnote 2 over S, H a locally free rank p ...
The Eigencurve of Modular Symbols SpringerLink
Webthis work was the construction of the rigid space known as the eigencurve ([9]). The existence of the eigencurve shows that the p-adic variation of certain residu-ally modular Galois representations can be interpreted automorphically. This has opened the door to a whole new field of study - a type of “p-adic” Langlands pro-gramme. WebThe 2-adic Eigencurve is Proper. Kevin Buzzard∗ Frank Calegari† July 5, 2005 1 Introduction In [7], Coleman and Mazur construct a rigid analytic space E that parameterizes overcon … neil\u0027s archery and crossbow
LOCAL TO GLOBAL COMPATIBILITY ON THE EIGENCURVE
WebThe eigencurve is a rigid analytic curve over Q_p parametrizing all finite slope overconvergent modular eigencurve. It is a conjecture of Coleman-Mazur that the eigencurve has "no holes". In other words, the eigencurve is proper over the weight space. We prove that the conjecture is true. No Notes/Supplements Uploaded No Video Files … WebIn number theory, an eigencurve is a rigid analytic curve that parametrizes certain p-adic families of modular forms, and an eigenvariety is a higher-dimensional generalization of … WebThe Eigencurve is Proper A dissertation presented by Hansheng Diao to The Department of Mathematics in partial ful llment of the requirements for the degree of Doctor of … neil\u0027s auto repair bethlehem ga