19 citations · 19 across the 4 of their papers we have counts for
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Asymptotic behavior of Tor over complete intersections and applications
Hailong Dao
Let be a local complete intersection and are -modules such that $\ell(\Tor_i^R(M,N))<\infty$ for . Imitating an approach by Avramov and Buchweitz, we investiga…
On injectivity of maps between Grothendieck groups induced by completion
Hailong Dao
We give an example of a local normal domain such that the map of Grothendieck groups $\G(R) \to \G(\hat R)$ is not injective. We also raise some questions about the kernel of t…
On liftable and weakly liftable modules
Hailong Dao
Let be a Noetherian ring and a nonzerodivisor on . We study concrete necessary and sufficient conditions for a module over to be weakly liftable to , in the…
Some observations on local and projective hypersurfaces
Hailong Dao
Let be a hypersurface in an equicharacteristic or unramified regular local ring. For a pair of modules over we study applications of rigidity of $\Tor^R(M,N)$, base…