2020/07/16 by Briggs, Benjamin, Iyengar, Srikanth B., Letz, Janina C. +1 · 1 citation
#13B10 (primary) #13D03 #13D09 #14A15 #14A30 (secondary) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2007.08562
It is proved that a map φ\colon R→ S of commutative noetherian rings that is essentially of finite type and flat is locally complete intersection if and only S is proxy small as a bimodule. This means that the thick subcategory generated by S as a module over the enveloping algebra S⊗RS contains a perfect complex supported fully on the diagonal ideal. This is in the spirit of the classical result that φ is smooth if and only if S is small as a bimodule, that is to say, it is itself equivalent to a perfect complex. The geometric analogue, dealing with maps between schemes, is also established. Applications include simpler proofs of factorization theorems for locally complete intersection maps.