AMS eBook CollectionsOne of the world's most respected mathematical collections, available in digital format for your library or institution
A Study in Derived Algebraic Geometry, Part 2: Volume II: Deformations, Lie Theory and Formal Geometry
About this Title
Dennis Gaitsgory, Harvard University, Cambridge, MA and Nick Rozenblyum, University of Chicago, Chicago, IL
Publication: Mathematical Surveys and Monographs
Publication Year:
2017; Volume 221.2
ISBNs: 978-1-4704-3570-7 (print); 978-1-4704-4087-9 (online)
DOI: https://doi.org/10.1090/surv/221.2
MathSciNet review: MR3701353
MSC: Primary 14F05; Secondary 18D05, 18G55
Table of Contents
Download chapters as PDF
Front/Back Matter
Inf-schemes
- Introduction
- Deformation theory
- Ind-schemes and inf-schemes
- Ind-coherent sheaves on ind-inf-schemes
- An application: Crystals
Formal geometry
- Introduction
- Formal moduli
- Lie algebras and co-commutative co-algebras
- Formal groups and Lie algebras
- Lie algebroids
- Infinitesimal differential geometry
- D. Arinkin and D. Gaitsgory, Singular support of coherent sheaves, and the geometric Langlands conjecture, Selecta Math. N.S. 21 (2015), 1–199.
- C. Barwick and C. Schommer-Pries, On the unicity of homotopy theory of higher categories, arXiv: 1112.0040.
- A. Beilinson and J. Bernstein, A proof of Jantzen’s conjectures, Advances in Soviet Mathematics 16, Part I (1993), 1–50.
- A. Beilinson and V. Drinfeld, Quantization of Hitchin?s integrable system and Hecke eigensheaves, available at http://www.math.harvard.edu/$\sim$gaitsgde/grad_2009/.
- R. Bezrukavnikov, On two geometric realizations of the affine Hecke algebra, arXiv:1209.0403.
- D. Benzvi, J. Francis and D. Nadler, Integral transforms and Drinfeld centers in derived algebraic geometry, J. Amer. Math. Soc. 23 (2010), no. 4, 909–966.
- R. Bezrukavnikov, On two geometric realizations of the affine Hecke algebra, arXiv:1209.0403.
- J. M. Boardman and J. M. Vogt Homotopy Invariant Structures on Topological Spaces, Lecture Notes in Mathematics 347, Springer-Verlag, Berlin and New York (1973).
- P. Deligne, Catégories tannakiennes, in: “The Grothendieck Festschrift”, Vol. II, 111–195, Progr. Math. 87, Birkhäuser Boston, Boston, MA, 1990.
- V. Drinfeld, DG Quotients of DG Categories, J. Algebra 272 (2004), no. 2, 643–691.
- V. Drinfeld and D. Gaitsgory, On some finiteness questions for algebraic stacks, GAFA 23 (2013), 149–294.
- V. Drinfeld and D. Gaitsgory, Compact generation of the category of D-modules on the stack of G-bundles on a curve, joint with V. Drinfeld, arXiv:1112.2402, Cambridge Math Journal, 3 (2015), 19–125.
- J. Francis, The tangent complex and Hochschild cohomology of $E_n$-rings, Compos. Math. 149 (2013), no. 3, 430–480.
- J. Francis and D. Gaitsgory, Chiral Koszul duality, Selecta Math. (N.S.) 18 (2012), 27–87.
- E. Frenkel and D. Gaitsgory, D-modules on the affine flag variety and representations of affine Kac-Moody algebras, Represent. Theory 13 (2009), 470–608.
- D. Gaitsgory, Ind-coherent sheaves, arXiv:1105.4857.
- D. Gaitsgory, The Atiyah-Bott formula for the cohomology of the moduli space of bundles on a curve, arXiv: 1505.02331.
- D. Gaitsgory, Sheaves of categories and the notion of 1-affineness, Contemporary Mathematics 643 (2015), 1–99.
- Notes on Geometric Langlands, Generalities on DG categories, available at http://www.math.harvard.edu/$\sim$gaitsgde/GL/.
- D. Gaitsgory and N. Rozenblyum, DG indschemes, Contemporary Mathematics 610 (2014), 139–251.
- D. Gaitsgory and N. Rozenblyum, D-modules and crystals, PAMQ 10, no. 1 (2014), 57–155.
- A. Joyal, Quasi-categories and Kan complexes, (in Special volume celebrating the 70th birthday of Prof. Max Kelly) J. Pure Appl. Algebra 175 (2002), no. 1-3, 207–222.
- A. Joyal, M. Tierney, Quasi-categories vs Segal spaces, Categories in algebra, geometry and mathematical physics, Contemp. Math. 431, Amer. Math. Soc., Providence, RI (2007), 277–326.
- H. Krause, The stable derived category of a Noetherian scheme, Compos. Math., 141(5) (2005), 1128–1162.
- G. Laumon, L. Morret-Baily, Champs algébriques, Ergebnisse der Mathematik und ihrer Grenzgebiete (3 Folge, A Series of Modern Surveys in Mathematics), 39, Springer-Verlag, Berlin, 2000.
- P. May, The geometry of iterated loop spaces, Lecture Notes in Mathematics 271, Springer-Verlag, Berlin and New York (1972).
- Y. Liu and W. Zheng, Enhanced six operations and base change theorem for Artin stacks, arXiv: 1211.5948.
- Y. Liu and W. Zheng, Gluing restricted nerves of infinity categories, arXiv: 1211.5294..
- J. Lurie, Higher Topos Theory, Annals of Mathematics Studies, 170, Princeton University Press, Princeton, NJ, 2009.
- J. Lurie, Higher Algebra, available at http://www.math.harvard.edu/$\sim$lurie.
- J. Lurie, $(\infty ,2)$-categories and Goodwillie calculus-I, available at http://www.math.harvard.edu/$\sim$lurie.
- J. Lurie, DAG-VII, Spectral schemes, available at http://www.math.harvard.edu/$\sim$lurie.
- J. Lurie, DAG-VIII, Quasi-Coherent Sheaves and Tannaka Duality Theorems, available at http://www.math.harvard.edu/$\sim$lurie.
- J. Lurie, DAG-X, Formal moduli problems, available at http://www.math.harvard.edu/$\sim$lurie.
- A. Neeman, The Grothendieck duality theorem via Bousfield techniques and Brown representability, J. Amer. Math. Soc. 9 (1996), no. 1, 205–236.
- C. Rezk, A model for the homotopy theory of homotopy theory, Trans. Amer. Math. Soc. 353 (2001), no. 3, 973–1007.
- C. Rezk, A Cartesian presentation of weak n-categories, Geom. Topol. 14 (2010), no. 1, 521–571.
- G. Segal, Categories and cohomology theories, Topology 13, (1974), 293–312.
- C. Simpson, Algebraic (geometric) $n$-stacks, arXiv: 9609014.
- B. Toen, Descente fidèlement plate pour les $n$-champs d’Artin.
- B. Toen and G. Vezzosi, Homotopical Algebraic Geometry-I.
- B. Toen and G. Vezzosi, Homotopical Algebraic Geometry-II.
- R. Thomason and T. Trobaugh, Higher algebraic K -theory of schemes and of derived categories, The Grothendieck Festschrift, Vol. III, 247–435, Progr. Math., 88 (1990).
- A. Yekutieli and J. Zhang, Dualizing Complexes and Perverse Sheaves on Noncommutative Ringed Schemes, Selecta Math. 12 (2006), 137–177.