Failure of Krull-Schmidt for invertible lattices over a discrete valuation ring
نویسندگان
چکیده
منابع مشابه
Fano Fibrations over a Discrete Valuation Ring
Using the Log minimal model program we construct nice models of del Pezzo fibrations which are relevant to the inductive study of del Pezzo fibrations. To investigate birational maps of Fano fibrations, we study elements in anticanonical linear systems of Fano varieties, which have the “worst” singularities. We also investigate certain special points on smooth hypersurfaces of degree n ≥ 3 in P...
متن کاملStandard Components of a Krull-schmidt Category
First, for a general Krull-Schmidt category, we provide criteria for an Auslander-Reiten component with sections to be standard. Specializing to the category of finitely presented representations of a strongly locally finite quiver and its bounded derived category, we obtain many new types of standard Auslander-Reiten components. Finally, specialized to the module category of a finite-dimension...
متن کاملKrull-schmidt Decompositions for Thick Subcategories
Following Krause [Kra99], we prove Krull-Schmidt theorems for thick subcategories of various triangulated categories: derived categories of rings, noetherian stable homotopy categories, stable module categories over Hopf algebras, and the stable homotopy category of spectra. In all these categories, it is shown that the thick ideals of small objects decompose uniquely into indecomposable thick ...
متن کاملKrull-schmidt Categories and Projective Covers
Krull-Schmidt categories are additive categories such that each object decomposes into a finite direct sum of indecomposable objects having local endomorphism rings. We provide a self-contained introduction which is based on the concept of a projective cover.
متن کاملLifting Lie Algebras over the Residue Field of a Discrete Valuation Ring
Let R be a discrete valuation ring with maximal ideal πR and residue field k. We study obstructions to lifting a Lie algebra L over R/πR to one over R/πR. If L̄ is the Lie algebra over k obtained from reducing L then we show there exists a well-defined class in H(L̄, ad) which vanishes if and only if L lifts. Furthermore, if L lifts, the lifts are shown to be in one to one correspondence with H(L̄...
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: 2005
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-05-08194-3