Example 78.7.2 (043K): Roots of unity as a group algebraic space

Processing math: 0%

Table of contents
Part 4: Algebraic Spaces
Chapter 78: Groupoids in Algebraic Spaces
Section 78.7: Examples of group algebraic spaces
Example 78.7.2: Roots of unity as a group algebraic space (cite)

Example 78.7.2 (Roots of unity as a group algebraic space). Let $B \to S$ as in Section 78.3. Let $n \in \mathbf{N}$ . Consider the functor which associates to any scheme $T$ over $B$ the subgroup of $\Gamma (T, \mathcal{O}_ T^*)$ consisting of $n$ th roots of unity. This is representable by the group algebraic space

$\mu _{n, B} = B \times _ S \mu _{n, S}$

over $B$ . Here $\mu _{n, S}$ is the group scheme of $n$ th roots of unity over $S$ , see Groupoids, Example 39.5.2.

The Stacks project

Comments (0)

Post a comment