The linear dual of the derived category of a scheme

de Salas, Carlos; de Salas, Fernando

doi:10.1090/S0002-9939-2011-10895-5

The linear dual of the derived category of a scheme
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by Carlos Sancho de Salas and Fernando Sancho de Salas PDF

Proc. Amer. Math. Soc. 139 (2011), 1897-1907 Request permission

Abstract:

Let $X\to S$ be a projective morphism of schemes. We study the category $D(X/S)^*$ of $S$-linear exact functors $D(X)\to D(S)$, and we study the Fourier transform $D(X)\to D(X/S)^*$.

References

Matthew Robert Ballard, Derived categories of sheaves of quasi-projective schemes, ProQuest LLC, Ann Arbor, MI, 2008. Thesis (Ph.D.)–University of Washington. MR 2712236
—, Equivalences of derived categories of sheaves on quasi-projective schemes, arXiv:0905.3148v2 [math.AG].
A. Bondal and M. van den Bergh, Generators and representability of functors in commutative and noncommutative geometry, Mosc. Math. J. 3 (2003), no. 1, 1–36, 258 (English, with English and Russian summaries). MR 1996800, DOI 10.17323/1609-4514-2003-3-1-1-36
Daniel Hernández Ruipérez, Ana Cristina López Martín, and Fernando Sancho de Salas, Relative integral functors for singular fibrations and singular partners, J. Eur. Math. Soc. (JEMS) 11 (2009), no. 3, 597–625. MR 2505443, DOI 10.4171/JEMS/162
Amnon Neeman, The Grothendieck duality theorem via Bousfield’s techniques and Brown representability, J. Amer. Math. Soc. 9 (1996), no. 1, 205–236. MR 1308405, DOI 10.1090/S0894-0347-96-00174-9
D. O. Orlov, Equivalences of derived categories and $K3$ surfaces, J. Math. Sci. (New York) 84 (1997), no. 5, 1361–1381. Algebraic geometry, 7. MR 1465519, DOI 10.1007/BF02399195
Dmitri D. Orlov and Valery A. Lunts, Uniqueness of enhancement for triangulated categories, J. Amer. Math. Soc. 23 (2010), 853–908.
Raphaël Rouquier, Dimensions of triangulated categories, J. K-Theory 1 (2008), no. 2, 193–256. MR 2434186, DOI 10.1017/is007011012jkt010