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SUMMARY:Duality of Drinfeld Modules and P-adic Properties of Drinfeld Mod
ular Forms
DTSTART;VALUE=DATE-TIME:20190605T083000Z
DTEND;VALUE=DATE-TIME:20190605T093000Z
DTSTAMP;VALUE=DATE-TIME:20210731T224355Z
UID:indico-event-4636@indico.math.cnrs.fr
DESCRIPTION:Let p be a rational prime\, $q>1$ a p-power and P a non-consta
nt irreducible polynomial in $F_q[t]$. The notion of Drinfeld modular form
is an analogue over $F_q(t)$ of that of elliptic modular form. Numerical
computations suggest that Drinfeld modular forms enjoy some P-adic struct
ures comparable to the elliptic analogue\, while at present their P-adic p
roperties are less well understood than the p-adic elliptic case. In 1990s
\, Taguchi established duality theories for Drinfeld modules and also for
a certain class of finite flat group schemes called finite $\\nu$-modules.
Using the duality for the latter\, we can define a function field analogu
e of the Hodge-Tate map. In this talk\, I will explain how the Taguchi's t
heory and our Hodge-Tate map yield results on Drinfeld modular forms which
are classical to elliptic modular forms e.g. P-adic congruences of Fourie
r coefficients imply p-adic congruences of weights.\n\nhttps://indico.math
.cnrs.fr/event/4636/
LOCATION:IHES Centre de confĂ©rences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/4636/
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