محفوظ في:
| المؤلفون الرئيسيون: | , , , |
|---|---|
| التنسيق: | Preprint |
| منشور في: |
2020
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| الموضوعات: | |
| الوصول للمادة أونلاين: | https://arxiv.org/abs/2002.12332 |
| الوسوم: |
إضافة وسم
لا توجد وسوم, كن أول من يضع وسما على هذه التسجيلة!
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جدول المحتويات:
- For a finite group $G$, we introduce a generalization of norm relations in the group algebra $\mathbb Q[G]$. We give necessary and sufficient criteria for the existence of such relations and apply them to obtain relations between the arithmetic invariants of the subfields of a normal extension of algebraic number fields with Galois group $G$. On the algorithmic side this leads to subfield based algorithms for computing rings of integers, $S$-unit groups and class groups. For the $S$-unit group computation this yields a polynomial time reduction to the corresponding problem in subfields. We compute class groups of large number fields under GRH, and new unconditional values of class numbers of cyclotomic fields.