Classifying Galois groups of small iterates via rational points
2018 ◽
Vol 14
(05)
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pp. 1403-1426
Keyword(s):
We establish several surjectivity theorems regarding the Galois groups of small iterates of [Formula: see text] for [Formula: see text]. To do this, we use explicit techniques from the theory of rational points on curves, including the method of Chabauty–Coleman and the Mordell–Weil sieve. For example, we succeed in finding all rational points on a hyperelliptic curve of genus 7, with rank 5 Jacobian, whose points parametrize quadratic polynomials with a “newly small” Galois group at the fifth stage of iteration.
2018 ◽
Vol 20
(04)
◽
pp. 1750038
1979 ◽
Vol 75
◽
pp. 121-131
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Keyword(s):
2020 ◽
Vol 16
(08)
◽
pp. 1767-1801
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1995 ◽
Vol 47
(6)
◽
pp. 1253-1273
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Keyword(s):
2019 ◽
Vol 2019
(754)
◽
pp. 87-141
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2018 ◽
Vol 2018
(736)
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pp. 69-93
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