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Finite ramification for preimage fields of post-critically finite morphisms
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Bridy, Andrew (författare)
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Ingram, Patrick (författare)
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Jones, Rafe (författare)
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Juul, Jamie (författare)
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- Levy, Alon (författare)
- KTH,Matematik (Inst.)
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Manes, Michelle (författare)
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Rubinstein-Salzedo, Simon (författare)
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Silverman, Joseph H. (författare)
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KTH Matematik (Inst) (creator_code:org_t)
- International Press of Boston, Inc. 2017
- Engelska.
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Ingår i: Mathematical Research Letters. - : International Press of Boston, Inc.. - 1073-2780 .- 1945-001X. ; 24:6, s. 1633-1647
- Relaterad länk:
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http://arxiv.org/pdf...
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https://urn.kb.se/re...
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https://doi.org/10.4...
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Abstract
Ämnesord
Stäng
- Given a finite endomorphism phi of a variety X defined over the field of fractions K of a Dedekind domain, we study the extension K (phi(-infinity)(alpha)) := boolean OR(n >= 1) K (phi(-n) (alpha)) generated by the preimages of alpha under all iterates of phi. In particular when phi is post-critically finite, i.e., there exists a non-empty, Zariski-open W subset of X such that phi(-1) (W) subset of W and phi : W -> X is etale, we prove that K (phi(-infinity) (alpha)) is rami fied over only finitely many primes of K. This provides a large supply of in finite extensions with restricted rami fication, and generalizes results of Aitken-Hajir-Maire [1] in the case X = A(1) and Cullinan-Hajir, Jones-Manes [7, 13] in the case X = P-1. Moreover, we conjecture that this finite rami fication condition characterizes post-critically finite morphisms, and we give an entirely new result showing this for X = P-1. The proof relies on Faltings' theorem and a local argument.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)