site stats

The eigencurve is proper

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 https://drntrucking.com

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

The eigencurve is proper — Princeton University

Category:The eigencurve is proper — Princeton University

Tags:The eigencurve is proper

The eigencurve is proper

Congruences between modular forms and the eigencurve construction

WebWe prove in this article that, for any prime p and tame level N, the projection from the eigencurve to the weight space satisfies a rigid analytic version of the valuative criterion for properness introduced by Buzzard and Calegari. WebThe 2-adic Eigencurve is Proper. Kevin Buzzard1 and Frank Calegari2 Received: August 25, 2005 Revised: February 27, 2006 Abstract. Coleman and Mazur ask whether the Eigencurve has any “holes”. We answer their question in the negative for the 2-adic Eigencurve of tame level one. 2000 Mathematics Subject Classification: 11F11, 14G35

The eigencurve is proper

Did you know?

WebWe prove that the Coleman–Mazur eigencurve is proper (over weight space) at integral weights in the center of weight space. 1. Introduction The eigencurveEis a rigid analytic … WebOct 23, 2024 · Some time later, Hansheng Diao and Ruochuan Liu proved that the eigencurve was indeed proper. There argument was completely different, and used local …

WebOct 15, 2015 · Congruences between modular forms (due to Shimura, Hida, etc) are really amazing. I know that the eigencurve construction are closely related to these relations. The basic reference is "The Eigencurve" by Coleman and Mazur. Besides, I think "A brief introduction to the work of Haruzo Hida" by Mazur is a good introduction.

WebWe prove in this article that, for any prime p and tame level N, the projection from the eigencurve to the weight space satisfies a rigid analytic version of the valuative criterion … WebWe prove that the Coleman–Mazur eigencurve is proper (over weight space) at integral weights in the center of weight space. 1 Introduction 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 [9], there have been

WebWe prove in this article that, for any prime p and tame level N, the projection from the eigencurve to the weight space satisfies a rigid analytic version of the valuative criterion …

WebOct 21, 2024 · We give a new proof of the properness of the Coleman-Mazur eigencurve. The question of whether the eigencurve satisfies the valuative criterion for properness was first asked by Coleman and Mazur in 1998 and settled by Diao and Liu in 2016 using deep, powerful Hodge- and Galois- theoretic machinery. Our proof is short and explicit and uses … neil\u0027s auto repair boynton beach flWebWe have to point out that although this property is named “properness of the eigencurve”, the projection πis actually not proper in the sense of rigid analytic geometry because it is of infinite degree. In the rest of the introduction we will sketch the steps to prove Theorem 1.1 and the structure of the paper. itm dyers pass roadWebJan 20, 2014 · The question was eventually resolved by Diao and Liu, who proved in 2014 ( [12]) that the eigencurve is indeed proper. Their proof is completely different from the … neil\u0027s bar and kitchenhttp://math.bu.edu/research/algebra/Spring2014/Diao-S2014.pdf neil\u0027s archery endicott nyWebThe Eigencurve is Proper. Doctoral dissertation, Harvard University. Abstract Coleman and Mazur constructed a rigid analytic curve Cp,N, called the eigencurve, whose points correspond to all finite slope overconvergent p-adic eigenforms. We prove the conjecture that the eigencurve Cp,N is proper over the weight space for any prime p and tame ... neil\u0027s barber shop blackheathWebJan 1, 2006 · The 2-adic eigencurve is proper Authors: Kevin Buzzard Frank Calegari 20+ million members 135+ million publication pages 2.3+ billion citations No full-text available … neil\u0027s bahr houstonWebMar 23, 2010 · The Eigencurve. 2. Geometric trends in Galois module theory. 3. Mixed elliptic motives. 4. On the Satake isomorphism. 5. Open problems regarding rational points on curves and varieties. 6. Models of Shimura varieties in mixed characteristics. 7. Euler systems and modular elliptic curves. 8. itmean.cn