TY - JOUR
T1 - The Minimal Ramification Problem for Rational Function Fields over Finite Fields
AU - Bary-Soroker, Lior
AU - Entin, Alexei
AU - Fehm, Arno
N1 - Publisher Copyright:
© 2023 Oxford University Press. All rights reserved.
PY - 2023/11/1
Y1 - 2023/11/1
N2 - We study the minimal number of ramified primes in Galois extensions of rational function fields over finite fields with prescribed finite Galois group. In particular, we obtain a general conjecture in analogy with the well studied case of number fields, which we establish for abelian, symmetric, and alternating groups in many cases.
AB - We study the minimal number of ramified primes in Galois extensions of rational function fields over finite fields with prescribed finite Galois group. In particular, we obtain a general conjecture in analogy with the well studied case of number fields, which we establish for abelian, symmetric, and alternating groups in many cases.
UR - http://www.scopus.com/inward/record.url?scp=85178060311&partnerID=8YFLogxK
U2 - 10.1093/imrn/rnac370
DO - 10.1093/imrn/rnac370
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AN - SCOPUS:85178060311
SN - 1073-7928
VL - 2023
SP - 18199
EP - 18253
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 21
ER -