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UID:news553@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20190114T101139
DTSTART;TZID=Europe/Zurich:20151008T161500
SUMMARY:Doktorkolloquium: Harry Schmidt
DESCRIPTION:For an elliptic curve E its additive extension is an algebraic
group G sitting inside an exact sequence of algebraic groups \\r\\n0→Ga
→G→E→0 \\r\\nwhere Ga is the additive group. The famous Manin-Mumf
ord conjecture\, proved by Hindry for such G\, states that the intersectio
n of a curve in G with its set of torsion points is finite unless the cur
ve is contained in an algebraic subgroup. We will present a relative vers
ion of this theorem for families of additive extensions. Afterwards we wi
ll discuss some consequences of this result for classical problems such a
s Pell’s equation in polynomials and elementary integration.
X-ALT-DESC:For an elliptic curve E its additive extension is an algebraic g
roup G sitting inside an exact sequence of algebraic groups \n0→Ga →G→E→0 \nwhere Ga is the additive group. The famous M
anin-Mumford conjecture\, proved by Hindry for such G\, states that the in
tersection of a curve in G with its set of torsion points is finite unles
s the curve is contained in an algebraic subgroup. We will present a rela
tive version of this theorem for families of additive extensions. Afterwa
rds we will discuss some consequences of this result for classical proble
ms such as Pell’s equation in polynomials and elementary integration.
DTEND;TZID=Europe/Zurich:20151008T171500
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