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SUMMARY:Tarun Dalal (IIT)
DTSTART:20220208T210000Z
DTEND:20220208T220000Z
DTSTAMP:20260423T024838Z
UID:UAANTS/34
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UAANTS/34/">
 The structure of Drinfeld modular forms of level $\\Gamma_0(T)$ and applic
 ations</a>\nby Tarun Dalal (IIT) as part of University of Arizona Algebra 
 and Number Theory Seminar\n\n\nAbstract\nLet $q$ be a power of an odd prim
 e $p$. Let $A:=\\mathbb{F}_q[T]$ and $C$ denote the completion of an algeb
 raic closure of $\\mathbb{F}_q((\\frac{1}{T}))$. For any ring $R$ with $A 
 \\subseteq R \\subseteq C$\, we let $M(\\Gamma_0(\\mathfrak{n}))_R$ denote
  the ring of Drinfeld modular forms of level $\\Gamma_0(\\mathfrak{n})$ wi
 th coefficients in $R$.\nIn 1988\, Gekeler showed that the $C$-algebra $M(
 \\mathrm{GL}_2(A))_C$ is isomorphic to $C[X\,Y]$. As a result\, the proper
 ties of the weight filtration for Drinfeld modular forms for $\\mathrm{GL}
 _2(A)$ are studied by Gekeler in 1988 and by Vincent in 2010.\n\nIn this t
 alk\, we discuss about the structure of the $R$-algebra $M(\\Gamma_0(T))_R
 $ and study the properties of the weight filtration for Drinfeld modular f
 orms of level $\\Gamma_0(T)$. As an application\, we prove a result on mod
 -$\\mathfrak{p}$ congruences for Drinfeld modular forms of level $\\Gamma_
 0(\\mathfrak{p} T)$ for $\\mathfrak{p} \\neq (T)$. This is a joint work wi
 th Narasimha Kumar.\n
LOCATION:https://researchseminars.org/talk/UAANTS/34/
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