Hailong Dao

Decent intersection and Tor-rigidity for modules over local hypersurfaces

First published in Transactions of the American Mathematical Society in 2013, published by the American Mathematical Society. Also available electronically from http://www.ams.org/journals/tran/2013-365-06/S0002-9947-2012-05574-7/home.html

Non-commutative resolutions and Grothendieck groups

Let

Projective dimension, graph domination parameters, and independence complex homology

R

Vanishing of Ext, cluster tilting modules and finite global dimension of endomorphism rings

be a noetherian normal domain. We investigate when

The radius of a subcategory of modules

R

Asymptotic behavior of Ext functors for modules of finite complete intersection dimension

admits a faithful module whose endomorphism ring has finite global dimension. This can be viewed as a non-commutative desingularization of

Some Homological Properties of Modules over a Complete Intersection, with Applications

\Spec(R)

ON THE RELATIONSHIP BETWEEN DEPTH AND COHOMOLOGICAL DIMENSION

. We show that the existence of such modules forces stringent conditions on the Grothendieck group of finitely generated modules over

Bounding the projective dimension of a squarefree monomial ideal via domination in clutters

R

Modules that detect finite homological dimensions

. In some cases those conditions are enough to imply that