The mock homotopy category of projectives and Grothendieck duality

By Daniel Murfet. 2007

87 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/844d9e0748b1df74bf124e23f4642a0e2d3c4405

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Hereditary abelian model categories (2015, methodology): “The geometric significance of Kex(Proj) is explained quite well in the Introduction to Murfet’s thesis [48].”
Exact model categories, approximation theory, and cohomology of quasi-coherent sheaves (2013, methodology): “The exact model categories give in many respects a complementary approach to that of dg algebras, with different advantages and weaknesses, and it has a good potential for instance in Gorenstein homological algebra [39], homological algebra in the category of quasi-coherent sheaves [22, 23, 28], or ”
Some adjoints in homotopy categories (2010, background): “In his thesis [9] Murfet defines the functor j WK.”
Deconstructibility and the Hill Lemma in Grothendieck categories (2010, background): “We aim to establish easy to use yet strong enough properties which cover a considerable part of technicalities tackled in the recent work of Gillespie, Estrada, Guil Asensio, Murfet, Neeman, Prest, Trlifaj and others; we refer to [13, 16, 17, 18, 23, 26, 29, 28].”
Support theory via actions of tensor triangulated categories (2011, background): “Their utility has been demonstrated in algebraic geometry, motivic theory, homotopy theory, modular representation theory, and noncommutative geometry: the theory of Grothendieck duality ([24], [27], [33], [35], [37]), Voevodsky’s motivic category ([32], [2]), Devinatz, Hopkins, and Smith’s work on ”
Coherent analogues of matrix factorizations and relative singularity categories (2011, result): “Notice that our proof is more akin to the arguments in [35, 34] than those of [15, 21] in that”
Approximations and adjoints in homotopy categories (2010, methodology): “The first result is an analogue of the flat cover conjecture for complexes of quasicoherent sheaves on a scheme; it has been established in the affine case by Neeman [33] and Enochs et al. [8], and for noetherian schemes by Murfet [29].”
Subcategories of singularity categories via tensor actions (2011, background): “lex of injectives. Note that tensoring a pure acyclic complex of ﬂats with a complex of injectives yields a contractible complex. This can be checked locally using [39] Corollary 9.7, see for example [34] Lemma 8.2. In particular every pure acyclic complex lies in the kernel of H. Deﬁnition 3.3. Wit”
On exact categories and applications to triangulated adjoints and model structures (2010, background): “A generalization of Example 4.15 for non-affine schemes was first studied by Murfet [47].”
Totally acyclic complexes over noetherian schemes (2009, methodology): “The main obstacle in developing the theory is the lack of projective quasi-coherent sheaves over non-affine schemes, which we solve using a recent construction of Neeman [Nee08], developed in the PhD thesis [Mur07] of the first author.”