Online (Cisco Webex https://futsunwei.my.webex.com/meet/ftwei)
Abstract:
Recently, Guan-Ting Chen and I established a function field analogue of the Ligozat–Newman theorem, providing a criterion for Drinfeld eta quotients on the Drinfeld modular curve $X_0(mathfrak{n})$ of arbitrary level $mathfrak{n}inmathbb{F}_q[T]$. We further conjecture that this criterion characterizes all Drinfeld eta quotients, and we verify this conjecture when $mathfrak{n}$ is square-free except for at most one prime divisor.
In the early 1970s, Andrew Ogg formulated several conjectures concerning rational torsion points on elliptic curves over $mathbb{Q}$ and on the Jacobians of modular curves. In this talk, we discuss function field analogues of these conjectures, their current status, and how our analogue of the Ligozat–Newman theorem can be applied to one of them.
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