数論幾何学セミナー:On p-adic analytic families of Hilbert eigenforms of finite slope over real quadratic fields and their applications

開催日時
2013年   8月 22日 10時 00分 ~ 2013年   8月 23日 16時 00分
場所
北海道大学理学部3号館413
講演者
山上 敦士
 
In this seminar, the speaker will talk about a construction of p-adic analytic families of Hilbert eigenforms of finite slope over real quadratic fields and their following two applications:

(I) The speaker will talk about a construction of an ''infinite fern'' in the universal deformation spaces over real quadratic fields, and show the Zariski density of Hilbert modular points in the ''parallel trace space'' using the ''twisted infinite fern''.

This result is a generalization of the results of Gouvea-Mazur, Boeckle and the speaker in the elliptic case.

(II) The speaker will also talk about p-adic analytic families of eigenforms of infinite slope.

Firstly, in the non-supercuspidal case, he will show how to construct a p-adic analytic family of eigenforms of infinite slope using a Coleman family of finite slope.

Secondly, in the supercuspidal case, he will show the non-existence of any p-adic analytic famliy of p-supercuspidal eigenforms using the base change method and p-adic analytic families of Hilbert eigenforms of finite slopes in the universal deformation space for the associated residual Galois representation over a suitable real quadratic field.

 

 

 

関連項目

研究集会・セミナー・集中講義の一覧へ