Detecting completeness from Ext-vanishing
نویسندگان
چکیده
منابع مشابه
On a non-vanishing Ext
The existence of valuation domains admitting non-standard uniserial modules for which certain Exts do not vanish was proved in [1] under Jensen’s Diamond Principle. In this note, the same is verified using the ZFC axioms alone. In the construction of large indecomposable divisible modules over certain valuation domainsR, the first author used the property thatR satisfied Ext1R(Q,U) 6= 0, where ...
متن کاملSymmetry Theorems for Ext Vanishing
It was proved by Avramov and Buchweitz that if A is a commutative local complete intersection ring with finitely generated modules M and N , then the Ext groups between M and N vanish from some step if and only if the Ext groups between N and M vanish from some step. This paper shows that the same is true under the weaker conditions that A is Gorenstein and that M and N have finite complete int...
متن کاملA Note on Symmetry in the Vanishing of Ext
In [1] Avramov and Buchweitz proved that for finitely generated modules M and N over a complete intersection local ring R, Ext R (M, N) = 0 for all i ≫ 0 implies ExtiR(N, M) = 0 for all i ≫ 0. In this note we give some generalizations of this result. Indeed we prove the above mentioned result when (1) M is finitely generated and N is arbitrary, (2) M is arbitrary and N has finite length and (3)...
متن کاملOf Module Structures , Vanishing of Ext , and Extended Modules
Let (R, m) and (S, n) be commutative Noetherian local rings, and let φ : R→ S be a flat local homomorphism such that mS = n and the induced map on residue fields R/m→ S/n is an isomorphism. Given a finitely generated R-module M , we show that M has an S-module structure compatible with the given R-module structure if and only if Ext R (S,M) = 0 for each i ≥ 1. We say that an S-module N is exten...
متن کاملSymmetry of Ext Vanishing over Non-commutative Rings
It is proved for certain graded non-commutative rings that if M and N are graded bi-modules, finitely generated from either side, then the Ext groups between M and N vanish from some step if and only if the Ext groups between N and M vanish from some step. Among the rings in question are twisted homogeneous coordinate rings of elliptic curves.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2008
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-08-09199-5