Zariski tangent space

《Solitons: Differential equations, symmetries, and infinite-dimensional algebras》 · 第 149–150 页 · Definition 6.2

Let $X$ be a scheme, and let $x\in X$. Then $\mathfrak m_x/\mathfrak m_x^2$ is a vector space over $\mathcal O_{X,x}/\mathfrak m_x=\kappa(x)$, and the (Zariski, or absolute) tangent space of $X$ at $x$ is by definition the dual vector space $T_xX=(\mathfrak m_x/\mathfrak m_x^2)^*$.