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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Basic Definition: Let R be a commutative ring with 1. A (unital) R-module is an abelian group M together with a operation R ×M → M , usually just written as rv when r ∈ R and v ∈ M . This operation is called scaling . The scaling operation satisfies the following conditions. 1. 1v = v for all v ∈M . 2. (rs)v = r(sv) for all r, s ∈ R and all v ∈M . 3. (r + s)v = rv + sv for all r, s ∈ R and all ...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 2012
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089512000407