Towards Hilbert's tenth problem for rings of integers through Iwasawa theory and Heegner points

被引：11

作者：

Garcia-Fritz, Natalia ^{[1
]}

Pasten, Hector ^{[1
]}

机构：

[1] Pontificia Univ Catolica Chile, Fac Matemat, Dept Matemat, 4860 Av Vicuna Mackenna, Macul, RM, Chile

来源：

MATHEMATISCHE ANNALEN | 2020年 / 377卷 / 3-4期

关键词：

ELLIPTIC-CURVES; DIOPHANTINE SETS; DERIVATIVES; VARIETIES; VALUES;

D O I：

10.1007/s00208-020-01991-w

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a positive proportion of primes p and q, we prove that Z is Diophantine in the ring of integers of Q( 3 v p, v -q). This provides a new and explicit infinite family of number fields K such that Hilbert's tenth problem for OK is unsolvable. Our methods use Iwasawa theory and congruences of Heegner points in order to obtain suitable rank stability properties for elliptic curves.

引用

页码：989 / 1013

页数：25

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