DC Field | Value | Language |
---|---|---|
dc.contributor.author | Koenig, Joachim | ko |
dc.date.accessioned | 2021-03-26T03:18:41Z | - |
dc.date.available | 2021-03-26T03:18:41Z | - |
dc.date.created | 2020-06-02 | - |
dc.date.issued | 2020-05 | - |
dc.identifier.citation | INTERNATIONAL JOURNAL OF NUMBER THEORY, v.16, no.4, pp.767 - 785 | - |
dc.identifier.issn | 1793-0421 | - |
dc.identifier.uri | http://hdl.handle.net/10203/282049 | - |
dc.description.abstract | This paper was motivated by a recent paper by Krumm and Pollack ([Twists of hyperelliptic curves by integers in progressions modulo p, preprint (2018); https://arXiv.org/abs/1807.00972]) investigating modulo-p behavior of quadratic twists with rational points of a given hyperelliptic curve, conditional on the abc-conjecture. We extend those results to twisted Galois covers with arbitrary Galois groups. The main point of this generalization is to interpret those results as statements about the sets of specializations of a given Galois cover under restrictions on the discriminant. In particular, we make a connection with existing heuristics about the distribution of discriminants of Galois extensions such as the Malle conjecture: our results show in a precise sense the non-existence of "local obstructions" to such heuristics, in many cases essentially only under the assumption that G occurs as the Galois group of a Galois cover defined over Q. This complements and generalizes a similar result in the direction of the Malle conjecture by Debts ([On the Malle conjecture and the self-twisted cover, Israel J. Math. 218(1) (2017) 101-131]). | - |
dc.language | English | - |
dc.publisher | WORLD SCIENTIFIC PUBL CO PTE LTD | - |
dc.title | On the mod-p distribution of discriminants of G-extensions | - |
dc.type | Article | - |
dc.identifier.wosid | 000531791800006 | - |
dc.identifier.scopusid | 2-s2.0-85074907416 | - |
dc.type.rims | ART | - |
dc.citation.volume | 16 | - |
dc.citation.issue | 4 | - |
dc.citation.beginningpage | 767 | - |
dc.citation.endingpage | 785 | - |
dc.citation.publicationname | INTERNATIONAL JOURNAL OF NUMBER THEORY | - |
dc.identifier.doi | 10.1142/S1793042120500396 | - |
dc.description.isOpenAccess | N | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | Galois extensions | - |
dc.subject.keywordAuthor | number fields | - |
dc.subject.keywordAuthor | discriminant | - |
dc.subject.keywordAuthor | distribution heuristics | - |
dc.subject.keywordAuthor | Galois covers | - |
dc.subject.keywordPlus | GALOIS | - |
dc.subject.keywordPlus | DENSITY | - |
dc.subject.keywordPlus | FIELDS | - |
dc.subject.keywordPlus | VALUES | - |
dc.subject.keywordPlus | RINGS | - |
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