Lecture Room B, 4th Floor, The 3rd General Building, NTHU
(清華大學綜合三館 4樓B演講室)
The Rational Torsion Subgroups of the Drinfeld Modular Jacobians for Prime-Power Levels
Sheng-Yang Ho (Pennsylvania State University)
Abstract
Fix a non-zero ideal
of
. Let
be the rational torsion subgroup of the Drinfeld modular Jacobian
. A generalized Ogg's conjecture states that
coincides with the rational cuspidal divisor class group
of the Drinfeld modular curve
. Recently, we proved that for any prime-power ideal
of
, the prime-to-
part of
is equal to that of
by studying the Hecke operators and the Eisenstein ideal of level
. Moreover, by relating the rational cuspidal divisors of degree
on
with
-quotients, where
is the Drinfeld discriminant function, we are able to compute explicitly the structure of
. As a result, the structure of the prime-to-
part of
is completely determined.
Organizer: Chieh-Yu Chang (NTHU)