Seminars

Overview : The main subjects of this course are the moduli stack of p-adic Galois representations (so-called the Emerton-Gee stack) and the theory of local models (developed by Le-Le Hung-Levin-Morra). The Emerton-Gee stack has its significance in the Langlands program. First, its local geometry is equivalent to the geometry of p-adic Galois deformation rings. Second, it provides a framework for the categorical p-adic local Langlands program recently proposed by Emerton-Gee-Hellmann. Therefore, it is desirable to understand the geometry of the Emerton-Gee stack. Although it is a highly complicated geometric object, the theory of local models provides concrete projective algebraic varieties whose singularities model those of the Emerton-Gee stacks. We will introduce these two subjects as well as some related topics. We will focus on conceptual understanding with a brief discussion of technical details. We hope to provide references to the subjects that can guide enthusiastic audiences to further studies.

For details, please refer to Heejong Lee.