|Date: Monday, January 24, 2022
Location: Virtual (3:00 PM to 4:00 PM)
Title: Comparison of Integral Structures on the Space of Modular Forms of Full Level N
Abstract: Let N≥3 and r≥1 be integers and p≥2 be a prime such that p∤N. One can consider two different integral structures on the space of modular forms over the rationals Q, one coming from arithmetic via q-expansions, the other coming from geometry via integral models of modular curves. Both structures are stable under the Hecke operators; furthermore, their quotient is finite torsion. Our goal is to investigate the exponent of the annihilator of the quotient. We will apply tools from Conrad to the situation of weight 2 and level Γ(Np^r) modular forms over Qp adjoin a Np^r root of unity to obtain an upper bound for the exponent. We also use Klein forms to construct explicit modular forms of level p, allowing us to compute a lower bound. When r=1, both bounds agree, allowing us to compute the exponent precisely in this case.
Speaker: Anthony Kling
Institution: University of Arizona
Event Organizer: Kartik Prasanna