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A note on asymptotically good extensions in which infinitely many primes split completely
Archiv der Mathematik ( IF 0.6 ) Pub Date : 2020-08-11 , DOI: 10.1007/s00013-020-01500-0
Oussama Hamza , Christian Maire

Let p be a prime number, and let K be a number field. For p=2, assume moreover K totally imaginary. In this note we prove the existence of asymptotically good extensions L{K of cohomological dimension 2 in which infinitely many primes split completely. Our result is inspired by a recent work of Hajir, Maire, and Ramakrishna [7].

中文翻译:

关于渐近良好扩展的注释,其中无限多个素数完全分裂

设 p 为素数,设 K 为数域。对于 p=2,还假设 K 完全是虚数。在这篇笔记中,我们证明了上同调维度 2 的渐近良好扩展 L{K 的存在,其中无限多个素数完全分裂。我们的结果受到 Hajir、Maire 和 Ramakrishna [7] 最近工作的启发。
更新日期:2020-08-11
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