Jakob Stix
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Titel: "Rational points and the arithmetic fundamental group"
Abstract:
The section conjecture of A. Grothendieck predicts that curves over
number fields whose arithmetic fundamental group extension splits will
have rational points. Period and index are invariants of a smooth
projective curve that have value 1 in the presence of a rational point.
We will examine the effect of the presence of a splitting on the
invariants period and index and will find examples where the section
conjecture holds "trivially" in an appropriate sense.