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Stable sets of primes in number fields | Alexander Ivanov
; | Date: |
11 Sep 2013 | Abstract: | We define a new class of sets -- stable sets -- of primes in number fields.
For example, Chebotarev sets $P_{M/K}(sigma)$, with $M/K$ Galois and $sigma
in Gal(M/K)$, are very often stable. These sets have positive (but arbitrary
small) Dirichlet density and generalize sets with density 1 in the sense that
arithmetic theorems like certain Hasse principles, the Grunwald-Wang theorem,
the Riemann’s existence theorem, etc. hold for them. Geometrically this allows
to give examples of infinite sets $S$ with arbitrary small positive density
such that $Spec mathcal{O}_{K,S}$ is algebraic $K(pi,1)$ (for all $p$
simultaneous). | Source: | arXiv, 1309.2800 | Services: | Forum | Review | PDF | Favorites |
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