Mathematics – Commutative Algebra
Scientific paper
2010-11-22
Mathematics
Commutative Algebra
12 pages
Scientific paper
We define a variant of Hochster's theta pairing and prove that it is constant in flat families of modules over hypersurfaces with isolated singularities. As a consequence, we show that the theta pairing factors through the Grothendieck group modulo algebraic equivalence. Moreover, our result allows us, in certain situations, to translate the properties of the theta pairing in characteristic zero to the characteristic p setting. We also give an application of our result to the rigidity of Tor over hypersurfaces.
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