PUB - Publikationen an der Universität Bielefeld

It is proved that a map φ:R→S of commutative Noetherian rings that is essentially of finite type and flat is locally complete intersection if and only if 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.