Topic
Exact sequence
About: Exact sequence is a research topic. Over the lifetime, 1531 publications have been published within this topic receiving 28565 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: In this paper, the authors re-prove Macaulay's theorem 4.11 is essentially equivalent to a suitable vanishing theorem for sheaf cohomology and give a proof of the de Rham algebraic theorem used in the proof of Theorem 5.3.
Abstract: In this section we want to re-prove the results of ?? 4 and 8 using sheaf cohomology. One reason for doing this is to clarify the discussion in those paragraphs and, in particular, to show how Macaulay's theorem 4.11 is essentially equivalent to a suitable vanishing theorem for sheaf cohomology. We shall also give a proof of the de Rham algebraic theorem used in the proof of Theorem 5.3. However, our principal motivation is to be able to discuss rational integrals in case our hypersurface V c P, has rather simple singularities, and the localization technique of sheaf theory seems to be the best method for doing this (cf. ?? 15, 16 below). Let then V c P, be a non-singular hypersurface. We want to give a sheaf-theoretic version of the Hodge filtration of Hq(V, C) (cf. ? 8). For this we let Qv be the sheaf on V of holomorphic q-forms and & c QV the subsheaf of closed forms. The Poincare' lemma for holomorphic differentials gives an exact sequence
761 citations
TL;DR: In this paper, a special class of cube complexes, called special cube-complexes, was introduced and examined, and it was shown that these complexes admit local isometries to the standard 2-complexs of naturally associated right-angled Artin groups.
Abstract: We introduce and examine a special class of cube complexes. We show that special cube-complexes virtually admit local isometries to the standard 2-complexes of naturally associated right-angled Artin groups. Consequently, special cube-complexes have linear fundamental groups. In the word-hyperbolic case, we prove the separability of quasiconvex subgroups of fundamental groups of special cube-complexes. Finally, we give a linear variant of Rips’s short exact sequence.
618 citations
TL;DR: In this article, a self-contained treatment of modules of finite G-dimension, established basic properties of relative and Tate cohomology, and embed the comparison morphisms into a canonical long exact sequence.
Abstract: We study finitely generated modules has finite projective dimension. Comparison morphisms and link these functors. We give a self-contained treatment of modules of finite G-dimension, establish basic properties of relative and Tate cohomology, and embed the comparison morphisms into a canonical long exact sequence . We show that these results provide efficient tools for computing old and new numerical invariants of modules over commutative local rings. 2000 Mathematical Subject Classification: 16E05, 13H10, 18G25.
478 citations
1 Jan 1998
TL;DR: The notes for a series of five lectures to the Barcelona Summer School in Commutative Algebra at the Centre de Recerca Matematica, Institut d'Estudis Catalans, July 15-26, 1996.
Abstract: This text is based on the notes for a series of five lectures to the Barcelona Summer School in Commutative Algebra at the Centre de Recerca Matematica, Institut d’Estudis Catalans, July 15–26, 1996
450 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 4 |
| 2024 | 9 |
| 2023 | 38 |
| 2022 | 40 |
| 2021 | 53 |
| 2020 | 60 |