Smoothness of Picard scheme of an abelian variety as in Mumford's book
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In Mumford's book, he shows $Pic^0$ of an abelian scheme is smooth by considering obstruction class:
why is the homomorphism $mu^*-p_1^*-p_2^*$ is injective on the second chomology? Mumford said in the last paragraph that we shall use structure of cohomology of abelian varieties (it's a wedge product of first cohomology) and Kunneth formula, but I don't know how to deduce the injectivity from those facts.
algebraic-geometry abelian-varieties
asked Nov 23 at 2:14
zzy
2,2231319
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up vote
2
down vote
favorite
In Mumford's book, he shows $Pic^0$ of an abelian scheme is smooth by considering obstruction class:
why is the homomorphism $mu^*-p_1^*-p_2^*$ is injective on the second chomology? Mumford said in the last paragraph that we shall use structure of cohomology of abelian varieties (it's a wedge product of first cohomology) and Kunneth formula, but I don't know how to deduce the injectivity from those facts.
algebraic-geometry abelian-varieties
asked Nov 23 at 2:14
zzy
2,2231319
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
In Mumford's book, he shows $Pic^0$ of an abelian scheme is smooth by considering obstruction class:
why is the homomorphism $mu^*-p_1^*-p_2^*$ is injective on the second chomology? Mumford said in the last paragraph that we shall use structure of cohomology of abelian varieties (it's a wedge product of first cohomology) and Kunneth formula, but I don't know how to deduce the injectivity from those facts.
algebraic-geometry abelian-varieties
asked Nov 23 at 2:14
zzy
2,2231319
In Mumford's book, he shows $Pic^0$ of an abelian scheme is smooth by considering obstruction class:
why is the homomorphism $mu^*-p_1^*-p_2^*$ is injective on the second chomology? Mumford said in the last paragraph that we shall use structure of cohomology of abelian varieties (it's a wedge product of first cohomology) and Kunneth formula, but I don't know how to deduce the injectivity from those facts.
algebraic-geometry abelian-varieties
algebraic-geometry abelian-varieties
asked Nov 23 at 2:14
zzy
2,2231319
asked Nov 23 at 2:14
zzy
2,2231319
asked Nov 23 at 2:14
zzy
2,2231319
asked Nov 23 at 2:14
zzy
2,2231319
asked Nov 23 at 2:14
zzy
2,2231319
2,2231319
add a comment |
add a comment |
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