Filter EXPLICIT GALOIS GROUPS OF INFINITE p-EXTENSIONS UNRAMIFIED AT p
نویسنده
چکیده
Galois groups of infinite p-extensions of number fields unramified at p are a complete mystery. We find by computer a family of pro-p groups that satisfy everything that such a Galois group must, and give evidence for the conjecture that these are the only such groups. This suggests that these mysterious Galois groups indeed have a specific form of presentation. There are surprising connections with knot theory and quantum field theory. Finally, the Fontaine-Mazur conjecture here reduces to a purely group-theoretic conjecture, and evidence for this conjecture and an extension of it is given.
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