Aws Lecture Notes: Modular Curves at Infinite Level
نویسنده
چکیده
These lectures concern the arithmetic of modular curves, and in particular the geometry of integral models of modular curves in the neighborhood of their singular points. These singularities only appear modulo p. If X is a modular curve and x is a singular point, then the nature of the singularity is measured by the completed local ring ÔX,x. Let us first review the basics of integral models of modular curves. Let Γ be one of the congruence subgroups Γ0(N), Γ1(N), or Γ(N). Then the modular curve X(Γ), a priori defined over Q, admits a smooth model over Z[1/N ]. That is, modular curves have good reduction modulo primes which do not divide the level. If p N , and if x ∈ X(Γ)(Fp) is a geometric point of the special fiber, then we have ÔX(Γ),x ∼= W JtK,
منابع مشابه
Modular Symbols and L-functions
As the rst non-overview lecture in this seminar, we will be setting up a lot of notation, getting comfortable working with modular symbols, and then hopefully discussing some of the major inputs which make the theory work. The rst half of the talk we will work through the example of the unique cusp form of weight two and level 11 on X0(11). In the second half, we will bring in the theoretical r...
متن کاملFactors affecting students tendency of Univercity students to Lecture Notes
Introduction: Many studies detected factors contributing to the students’ tendency to lecture notes. This study aimed at evaluating the factors affecting students tendency to lecture notes in Hormozgan University of Medical Sciences. Methods: In this descriptive study, 179 students from medicine, nursing & midwifery, health, and Paramedicine schools were selected through stratified random...
متن کاملAbstraction and Modular Verification of Infinite-State Reactive Systems
ion and Modular Verification of Infinite-State Reactive Systems ⋆ Zohar Manna, Michael A. Colón, Bernd Finkbeiner, Henny B. Sipma and Tomás E. Uribe Computer Science Department Stanford University Stanford, CA. 94305-9045 [email protected] Abstract. We review a number of temporal verification techniques for reactive systems using modularity and abstraction. Their use allows the verification...
متن کاملSiegel Modular Forms
These are the lecture notes of the lectures on Siegel modular forms at the Nordfjordeid Summer School on Modular Forms and their Applications. We give a survey of Siegel modular forms and explain the joint work with Carel Faber on vector-valued Siegel modular forms of genus 2 and present evidence for a conjecture of Harder on congruences between Siegel modular forms of genus 1 and 2.
متن کامل