分野別セミナー

Work of Shimura, Langlands, Milne-Shih, and, more recently, Taylor have examined the action of complex conjugation on Shimura varieties. We study this topic from the viewpoint of the general theory of these varieties, with the goal of establishing, in all applicable cases where the canonical field of definition E is complex, descents of the system of varieties to the maximal totally real subfield E^+ of E. We also study the reciprocity law for the connected components of the variety, and the reciprocity law at the CM points. We plan to conclude by mentioning the problem of integral models, and zeta functions, of these descended systems. The work is joint with Lucio Guerberoff (UCLA) and remains in progress.