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Greg Kuperberg
Greg Kuperberg
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Why havedo modules with small support have high extsExts?

Let $M$ be a module over a ring $R$. In nice situations (though I don't know what exactly nice means...) the following two numbers are equal:

1.) The codimension of the support of $M$

2.) The biggest $k$ such that $ext^k(M,.)$$\text{Ext}^k(M,.)$ doesn't vanish

Why do we expect this intuitively? Why should lenghtslengths of injective/projective/flat resolutions have anything to do with the support?

Why have modules with small support high exts?

Let $M$ be a module over a ring $R$. In nice situations (though I don't know what exactly nice means...) the following two numbers are equal:

1.) The codimension of the support of $M$

2.) The biggest $k$ such that $ext^k(M,.)$ doesn't vanish

Why do we expect this intuitively? Why should lenghts of injective/projective/flat resolutions have anything to do with the support?

Why do modules with small support have high Exts?

Let $M$ be a module over a ring $R$. In nice situations (though I don't know what exactly nice means...) the following two numbers are equal:

1.) The codimension of the support of $M$

2.) The biggest $k$ such that $\text{Ext}^k(M,.)$ doesn't vanish

Why do we expect this intuitively? Why should lengths of injective/projective/flat resolutions have anything to do with the support?

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Jan Weidner
Jan Weidner
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Why have modules with small support high exts?

Let $M$ be a module over a ring $R$. In nice situations (though I don't know what exactly nice means...) the following two numbers are equal:

1.) The codimension of the support of $M$

2.) The biggest $k$ such that $ext^k(M,.)$ doesn't vanish

Why do we expect this intuitively? Why should lenghts of injective/projective/flat resolutions have anything to do with the support?