Acyclicity of Tate constructions

✍ Scribed by Srikanth Iyengar

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 124 KB
• Volume: 163
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(00)00165-1

✦ Synopsis

We prove that a Tate construction A u1; : : : ; un | @(ui) = zi over a di erential graded algebra A, on cycles z1; : : : ; zn in A ≥1 , is acyclic if and only if the map of graded-commutative algebras H0(A)[y1; : : : ; yn] → H(A), with yi → cls(zi), is an isomorphism. This is used to establish that if a large homomorphism R → S has an acyclic closure R U with sup{i | Ui = ∅} = s ¡ ∞, then s is either 1 or an even integer.