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{\Large Department of Mathematics, BGU}

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{\Huge Jerusalem - Be'er Sheva Algebraic Geometry Seminar}\\[0.2\baselineskip]

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\textbf{On} \emph{Wednesday, December 23, 2020}
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\textbf{At} \emph{15:00 -- 16:30}
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\textbf{In} \emph{}

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{\large\scshape Mihran Papikian 
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  (Pennsylvania State University)
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will talk about
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{\Large\bfseries Drinfeld discriminant function and Fourier expansion of harmonic cochains\par}
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\textsc{Abstract:}
I will discuss my joint work with Fu-Tsun Wei from Tsing Hua University in Taiwan.

Let \$K\$ be the completion of \$\textbackslash{}mathbb\{F\}\_q(T)\$ at \$1/T\$ and \$r\textbackslash{}geq 2\$ be an integer. In an ongoing project, we study modular units on the Drinfeld symmetric space \$\textbackslash{}Omega\^{}r\$ over \$K\$, harmonic cochains on the edges of the Bruhat-Tits building of \$PGL\_r(K)\$, and the cuspidal divisor groups of certain Drinfeld modular varieties of dimension \$r-1\$. In particular, we obtained a higher dimensional analogue of a well-known result of Ogg for classical modular curves \$X\_0(p)\$ of prime level.








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