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 … WebWe 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.

The eigencurve is proper — Princeton University

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. 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 … gold standard hiv

The eigencurve is proper - math.bu.edu

WebThe Eigencurve is Proper. Doctoral dissertation, Harvard University. Abstract Coleman and Mazur constructed a rigid analytic curve Cp,N, called the eigencurve, whose points … 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 … WebMar 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. gold standard history united states