proregular
adjEtymology From pro- + regular.
1
Mathematics, Sciences Having the property that the inverse systems of the Koszul cohomology modules satisfy the Inverse limit#Mittag-Leffler condition.)
- Then adic reduction to the diagonal holds: A#92;otimes#123;L#125;#95;#123;A#92;hat#123;#92;otimes#125;#123;L#125;#95;#123;K#125;A#125;(M#92;hat#123;#92;otimes#125;#123;L#125;#95;#123;K#125;N)#92;congM#92;otimes#123;L#125;#95;AN. (2) Let A be a commutative ring, let a#92;subseteqA be a weakly proregular ideal, let M be an A-module, and assume that the a-adic completion of A is noetherian (if A is noetherian, all these conditions are always satisfied).2016, Liran Shaul, “Adic reduction to the diagonal and a relation between cofiniteness and derived completion”, in arXiv: