# Tagged Questions

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### Invariant differentials on group schemes

I'm studying group schemes from http://www.math.ru.nl/~bmoonen/BookAV/BasGrSch.pdf and I have some trouble with the following proposition. (3.15)Proposition Let $\pi:G\to S$ be a group scheme. Then ...
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### Connected scheme but not quasicompact

I am searching for a connected scheme which is not quasi compact. My try: Suppose $A_i$=Spec$k[x]$, where $k$ is algebraically closed field are affine schmes . I am planning to glue $0$ of the ...
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### Sheaf of ideals [duplicate]

Let $(X, \mathcal{O}_X)$ be a scheme and and $f \in \mathcal{O}_X(X)$. We define the sheaf of ideals by the assignment $$U \longmapsto f|_U \mathcal{O}_X(U)$$ and denote this sheaf by ...
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### Equivariant Sheaves, Local system

Let $(G,m)$ be a group scheme unipotent, and $L$ a local system of rank 1 on $G$ such that: $m^*(L) \simeq L \boxtimes L$. Then why is $L$ an equivariant sheaf on $G$ with the action the ...
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### Lifting sheaves from the special fibre to the generic fibre

Let $R$ be a complete discrete valuation ring and let $S = \operatorname{Spec}(R)$. Let $\mathcal{X}\to S$ be a complete, regular, flat, connected $S$-scheme of finite type whose fibres are smooth, ...
I have a question more about terminology than anything else: If $f:X\rightarrow Y$ is an isomorphism of schemes, then what does it mean to say "the invertible sheaf $\mathscr{L}$ on $X$ corresponds ...
Suppose we have two schemes $X, Y$ and a map $f: X\to Y$. Then we know that $\operatorname{Hom}_X(f^*\mathcal{G}, \mathcal{F})\simeq \operatorname{Hom}_Y(\mathcal{G}, f_*\mathcal{F})$, where ...