منابع مشابه
A Kleiman–beritini Theorem for Sheaf Tensor Products
Fix a variety X with a transitive (left) action by an algebraic group G. Let E and F be coherent sheaves on X . We prove that for elements g in a dense open subset of G, the sheaf TorXi (E , gF) vanishes for all i > 0. When E and F are structure sheaves of smooth subschemes of X in characteristic zero, this follows from the Kleiman–Bertini theorem; our result has no smoothness hypotheses or hyp...
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Fix a variety X with a transitive (left) action by an algebraic group G. Let E and F be coherent sheaves on X . We prove that for elements g in a dense open subset of G, the sheaf Tor i (E , gF) vanishes for all i > 0. When E and F are structure sheaves of smooth subschemes of X in characteristic zero, this follows from the Kleiman–Bertini theorem; our result has no smoothness hypotheses on the...
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Let R be a commutative ring and M and N be R-modules. (We always work with rings having a multiplicative identity and modules are assumed to be unital: 1 ·m = m for all m ∈M .) The direct sum M ⊕N is an addition operation on modules. We introduce here a product operation M ⊗RN , called the tensor product. We will start off by describing what a tensor product of modules is supposed to look like....
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 2004
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089504001776