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April 7
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Utrecht Room K11 (basement)
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11:30-12:20
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Marco Streng, Elliptic divisibility sequences with complex
multiplication
Abstract.
A classical elliptic divisibility sequence (indexed by the integers)
arises as denominators of the multiples of a fixed rational point of
infinite order on an elliptic curve over the rationals. Such a
sequence is knownto have primitive divisors from some point on (as
follows from height estimates and Siegel's theorem). If the curve has
complex multiplication, we show how the cm-ring can be used to index a
similar sequence of ideals and prove that it has primitive divisors.
The classical proof breaks down and needs to be replaced by an
inclusion/exclusion proof with finer diophantine estimates involving
ellipticlogarithms
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13:30-14:20 |
Gunther Cornelissen, Deformations of weakly ramified
coverings of curves
Abstract.
A cover of curves over a field of characteristicp is said to be weakly
ramified if all second ramification groups vanish. I will discuss work
with Ariane Mézard that computes the (mixed-characteristic)
universal deformation ring of such a cover. Using previous work with
Bertin and Kato, one only needs to determine the characteristic of
that ring, which turns out to be either p or zero.
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14:30-15:20 |
Jakub Byszewski, A universal deformation ring that is not a
complete intersection
Abstract.
Bleher and Chinburg recently gave an example of a linear
representation of a finite group whose universal deformation ring is
not a complete intersection, thus answering a question of Flach. Their
proof uses some modular representation theory. We will show that the
same result can be proven using only standard cohomological
obstruction calculus.
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15:40-16:30 |
Oliver Lorscheid, Toroidal integrals
Abstract.
In the 1970's, Don Zagier developed the formalism of toroidal
automorphic forms, where the usual parabolic condition is substituted
by the vanishing of integrals over various tori. We will outline the
relation between these spaces and zeros of zeta functions (via
Eisenstein series and Tate's thesis), paying particular attention to
the case of a split torus (left somewhat aside in the original work)
and to explicit calculation of such integral vanishing conditions in
the case of global function fields.
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