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ON THE NILPOTENT SECTION CONJECTURE FOR FINITE GROUP ACTIONS ON CURVES
Author(s) -
Pál Ambrus
Publication year - 2014
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s002557931300017x
Subject(s) - mathematics , section (typography) , conjecture , nilpotent , prime (order theory) , pure mathematics , locally nilpotent , group (periodic table) , combinatorics , finite group , order (exchange) , nilpotent group , discrete mathematics , algebra over a field , chemistry , organic chemistry , finance , advertising , economics , business
We give a new, geometric proof of the section conjecture for fixed points of finite group actions on projective curves of positive genus defined over the field of complex numbers, as well as its natural nilpotent analogue. As a part of our investigations we give an explicit description of the abelianised section map for groups of prime order in this setting. We also show a version of the 2‐nilpotent section conjecture.