WorkshopsWeight-raising without Hasse invariants
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A modular form of weight two and level N, prime-to-p, is congruent mod p to a weight p+1 form of the same level N. This is proved by multiplication by a classical Eisenstein series E, a characteristic zero lift of the Hasse invariant. A different proof by Edixhoven and Khare avoids the use of E, and gives analogous congruences for GL(2) over imaginary quadratic fields and over certain totally real fields, in which p is inert. We will apply this trick to definite unitary groups U(n), by invoking a result of Bardoe and Sin.
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Claus Sørensen
2010-07-16
14:00:00 - 15:20:00
101 , Mathematics Research Center Building (ori. New Math. Bldg.)
A modular form of weight two and level N, prime-to-p, is congruent mod p to a weight p+1 form of the same level N. This is proved by multiplication by a classical Eisenstein series E, a characteristic zero lift of the Hasse invariant. A different proof by Edixhoven and Khare avoids the use of E, and gives analogous congruences for GL(2) over imaginary quadratic fields and over certain totally real fields, in which p is inert. We will apply this trick to definite unitary groups U(n), by invoking a result of Bardoe and Sin.