# Questions tagged [picard-scheme]

In algebraic geometry, the scheme that represents the Picard functor and the natural generalisation of the Picard variety for a given algebraic variety to the theory of schemes. If your question is not about algebraic or arithmetic geometry, then this is likely not the right tag to use.

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### "Universal" line bundle over the Picard variety $\operatorname{Pic}^0(X)$.

$\DeclareMathOperator{\Pic}{Pic}$This question is inspired by my attempt to answer another question. At the end of my answer, there is a missing step, which I don't know how to fill. Let $X$ be a ...
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### Embedding of Picard functor into $\text{Hom}_k(-,\text{Pic}(X/k))$

$\DeclareMathOperator\Hom{Hom}\DeclareMathOperator\Pic{Pic}\DeclareMathOperator\Spec{Spec}\DeclareMathOperator\pr{pr}$ Let $X$ be an algebraic variety $X$, that is proper over $k$ (here a variety is a ...
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### Inversion of an element in Picard group over commutative ring

I'm having some troubles understanding a proof in Commutative Algebra Chapter I - VII of N. Bourbaki. It's on pag 114 of the book. Here's what it says: Theorem 3 ... (ii) Conversely, if $M$ is an $A-$...
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### Picard group schemes of degree d

Let $C$ be a smooth curve. I know that $Pic^0(C)$, i.e. the Picard group of degree 0 line bundles on $C$, is isomorphic to the jacobian $J(C)$, so it is an abelian variety. My question is, what about \$...
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### Group law for an elliptic curve using schemes

I was trying to understand better the definition of the group law for an elliptic curve given in Katz and Mazur's book (http://books.google.com.br/books/about/Arithmetic_Moduli_of_Elliptic_Curves.html?...
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