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 qexpansions, 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.
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Speaker: Anthony Kling
Institution: University of Arizona
Event Organizer: Kartik Prasanna
