Grothendieck Duality and Base Change

By Brian Conrad. 2001

290 citations recorded by the source corpus.

Subfields: Geometry and Topology, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/707f6f74c68cf597e86f3ea730b77e43706060e6

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In Geometry and Topology

In Theoretical Computer Science

Citations in the corpus

Reduction of derived Hochschild functors over commutative algebras and schemes (2009, background): “The second one involves fundamental results of Grothendieck duality theory, systematically developed in [15, 11, 19]; the relevant notions and theorems are reviewed in Section 5.”
Characteristic classes of mixed Hodge modules (2009, background): “MHC y(·)) : K0(MHM(Z)) → G0(Z)⊗Z[y±1]. Note that for Z = pt a point this reduces to the duality formula (14) for the χ y-genus. For dualizing complexes and (relative) Grothendieck duality we refer to [25, 16, 32] as well as [23][Part I,sec. 7]). Note that for M smooth of pure dimension m, one has ω ”
On a non-vanishing conjecture of Kawamata and the core of an ideal (2003, unknown): “See also [5].”
The canonical sheaf of Du Bois singularities (2008, background): “s in a smooth variety, this determines the dualizing complex on any such ﬁnite type scheme. Alternatively, one can also deﬁne ω q X as h !C where h : X → C is the structural morphism. See [Har66] and [Con00] for details. For an equidimensional X admitting a dualizing complex one may deﬁne the canoni”
Reflexive pull-backs and base extension (2004, background): “We refer the reader to [3] for a recent account of relative duality.”
Topics in classical algebraic geometry (2006, methodology): “Now we apply Grothendieck’s Duality Theorem (see [57]) to obtain a natural isomorphism of sheaves”
F-singularities via alterations (2011, background): “In general this is a difficult and subtle issue (see [Con00]); however, we will only need this for open inclusions U ⊆X and localization at a point, where it is not problematic.”
Grothendieck Duality for Deligne-Mumford Stacks (2008, methodology): “(g◦f)♯. The isomorphism ζf,g can be chosen to be the isomorphism in [Har66, III Def 1.5]. The statement is the same as in Residues and Duality but we have applied the sign ﬁxing proposed by Conrad in [Con00]. At this level the isomorphism ζf,g appears to be completely arbitrary, nonetheless it becom”