A Review on Drinfeld modular forms of Hecke operators
Keywords:
Drinfeld modular forms, Reduction of Drinfeld modular forms modulo T.Abstract
In this newspaper we determine the explicit composition of the semi simple part of the Hecke algebra that works on Drinfeld modular kinds of full level modulo T. We show that modulo T the Hecke algebra has a non-zero semi simple part. On the other hand, a well-known theorem of Serre asserts that for traditional modular varieties the action of Tl for any peculiar primary l is nilpotent modulo 2. After showing the effect for Drinfeld modular varieties modulo T, we use computations of the Hecke action modulo T showing that certain forces of the Drinfeld modular form h can't be Eigen forms. Finally, we conjecture that the Hecke algebra that functions on Drinfeld modular varieties of full level is not soft for large weight, which again contrasts the traditional situation.
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