The Chevalley-Gras formula over global fields

A remark on Chevalley's ambiguous class number formulas

In this note we remark that Chevalley's ambiguous class number formula is an immediate consequence of the Hasse norm theorem, the local and global norm index theorems for cyclic extensions.

Chevalley's class number formula, unit equations and the asymptotic Fermat's Last Theorem

Let $F$ be a number field and $\mathcal{O}_F$ its ring of integers. We use Chevalley's ambiguous class number formula to give a criterion for the non-existence of solutions to the unit equation $λ+ μ= 1$, $λ, μ\in \mathcal{O}_F^\times$. This is then used to strengthen a criterion for the asymptotic Fermat's Last Theorem due to Freitas and Siksek.

The Chevalley-Weil Formula for Orbifold Curves

In the 1930s Chevalley and Weil gave a formula for decomposing the canonical representation on the space of differential forms of the Galois group of a ramified Galois cover of Riemann surfaces. In this article we prove an analogous Chevalley-Weil formula for ramified Galois covers of orbifold curves. We then specialize the formula to the case when the base orbifold curve is the (reduced) modular orbifold. As an application of this latter formula we decompose the canonical representations of modular curves of full, prime level and of Fermat curves of arbitrary exponent.

Chevalley's ambiguous class number formula for an arbitrary torus

This version is a significant improvement of the original paper. It includes a new section where we discuss norm tori in some detail. The new abstract is the following: In this paper we obtain Chevalley's ambiguous class number formula for an arbitrary torus T over a global field. The classical formula of C.Chevalley may be recovered by setting T=G_{m} in our formula. As an illustration of the general result, we discuss norm tori in detail. A key ingredient of the proof of our main theorem is the work of X.Xarles on groups of components of Neron-Raynaud models of tori.

Chevalley - Herbrand公式与p - 主虚二次域的Z_p - 扩张

Chevalley-Herbrand formulas and Zp -extensions of a p-principal imaginary quadratic field

研究虚二次域k在特定条件下的Z_p - 扩张，通过Chevalley - Herbrand公式推广及p - 进调节器性质，得出不同e值下λ(K/k)、μ(K/k)的结论，给出有效可计算结果并提供相关计算程序。

Chevalley–Herbrand 公式与实 Abel 主猜想

The Chevalley-Herbrand formula and the real abelian Main Conjecture

本文利用 Chevalley–Herbrand 公式与类群在辅助 p 扩张中的投降现象，建立其同实 Abel 主猜想的联系，证明投降可推出该猜想，并以 PARI 计算支持。