Abstract
We define a variant of Hochster’s θ pairing and prove that it is constant in flat families of modules over hypersurfaces with isolated singularities. As a consequence, we show that the θ pairing factors through the Grothendieck group modulo algebraic equivalence. Moreover, our result allows us, in certain situations, to translate the properties of the θ pairing in characteristic zero [established in Moore et al. (Adv Math, 226(2):1692–1714, 2011) and Polishchuk and Vaintrob (Chern characters and Hirzebruch–Riemann-Roch formula for matrix factorizations. Preprint, arXiv:1002, 2010)] to the characteristic p setting. We also give an application of our result to the rigidity of Tor over hypersurfaces.
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