## 43.2 Conventions

We fix an algebraically closed ground field $\mathbf{C}$ of any characteristic. All schemes and varieties are over $\mathbf{C}$ and all morphisms are over $\mathbf{C}$. A variety $X$ is nonsingular if $X$ is a regular scheme (see Properties, Definition 28.9.1). In our case this means that the morphism $X \to \mathop{\mathrm{Spec}}(\mathbf{C})$ is smooth (see Varieties, Lemma 33.12.6).

## Comments (1)

Comment #4864 by Matthieu Romagny on

I find the choice of the letter $\mathbb{C}$ for the algebraically closed field quite confusing. I happened to be reading parts of this chapter without prior knowledge of the conventions section, and it really puzzled me. Why not just $k$?

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