I do not know if this counts as number theory, but I came to this question while studying number theory, so I post this here.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose X and Y are reduced schemes of finite type over a field k and f:X->Y is a morphism. Ox denotes the structural sheaf of X.

Question

What is a stalk of the direct image sheaf f[tex]_{*}[/tex]Ox at y in Y?

Since this question is too general, here is a specific question I encountered.

In addition to the assumptions above, let f be flat and y be a generic point of some irreducible component of Y. In this case, is f[tex]_{*}[/tex]Ox[tex]_{y}[/tex] isomorphic to the direct sum of Ox[tex]_{x}[/tex], where x runs through the preimage of y?

Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Direct Image Sheaf

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**