Topological methods for complex-analytic Brauer groups
Tài liệu tham khảo
Y. Abe, K. Kopfermann, Toroidal Groups, Lecture Notes in Mathematics, vol. 1759, Springer, Berlin, 2001.
Barth, 1984, Compact complex surfaces, Ergeb. Math. Grenzgeb., 4
Berkovič, 1972, The Brauer group of abelian varieties, Funksional. Anal. Priložen., 6, 10
Bogomolov, 1976, Classification of surfaces of class VII0 with b2=0, Izv. Akad. Nauk SSSR Ser. Mat., 40, 273
Bott, 1986, Differential forms in algebraic topology, Grad. Texts Math., 82
V. Brînzănescu, Holomorphic vector bundles over compact complex surfaces, Lecture Notes in Mathematics, vol. 1624, Springer, Berlin, 1996.
Browder, 1961, Torsion in H-spaces, Ann. Math., 74, 24, 10.2307/1970305
Carlson, 1997, On fundamental groups of class VII surfaces, Bull. London Math. Soc., 29, 98, 10.1112/S0024609396001774
P. Deligne, Cohomologie étale. SGA 412, Lecture Notes in Mathematics, vol. 569, Springer, Berlin, 1977.
G. Dethloff, H. Grauert, Seminormal complex spaces, in: H. Grauert, T. Peternell, R. Remmert (Eds.), Several Complex Variables, vol. VII, Encyclopaedia of Mathematical Sciences, vol. 74, Springer, Berlin, 1994, pp. 183–220.
Dloussky, 1984, Structure des surfaces de Kato, Mém. Soc. Math. France, 14
Dloussky, 2000, Surfaces de la classe VII0 admettant un champ de vecteurs, Comment. Math. Helv., 75, 255, 10.1007/PL00000374
Dloussky, 2003, Class VII0 surfaces with b2 curves, Tohoku Math. J., 55, 283, 10.2748/tmj/1113246942
Edidin, 2001, Brauer groups and quotient stacks, Amer. J. Math., 123, 761, 10.1353/ajm.2001.0024
Elencwajg, 1983, Projective bundles on a complex torus, J. Reine Angew. Math., 340, 1
Freitag, 1988, Étale cohomology and the Weil conjecture, Ergeb. Math. Grenzgeb., 13
O. Gabber, Some theorems on Azumaya algebras, in: M. Kervaire, M. Ojanguren (Eds.), Groupe de Brauer, Lecture Notes in Mathematics, vol. 844, Springer, Berlin, 1981, pp. 129–209.
Giraud, 1971, Cohomologie non abélienne, Grundlehren Math. Wiss., 179, 10.1007/978-3-662-62103-5
Godement, 1964
Grothendieck, 1968, Le groupe de Brauer I, 46
Grothendieck, 1968, Le groupe de Brauer II, 67
Grothendieck, 1968, Le groupe de Brauer III, 88
A. Grothendieck, et al., Théorie des topos et cohomologie étale, Tome 3, Lecture Notes in Mathematics, vol. 305, Springer, Berlin, 1973.
Hamm, 1983, Zum Homotopietyp Steinscher Räume, J. Reine Angew. Math., 338, 121, 10.1515/crll.1983.338.121
Hironaka, 1975, Flattening theorem in complex-analytic geometry, Amer. J. Math., 97, 503, 10.2307/2373721
Hochschild, 1953, Cohomology of group extensions, Trans. Amer. Math. Soc., 74, 110, 10.1090/S0002-9947-1953-0052438-8
Hoobler, 1972, Brauer groups of abelian schemes, Ann. Sci. École Norm. Sup., 5, 45, 10.24033/asens.1220
Huppert, 1967, Endliche Gruppen I, Grundlehren Math. Wiss., 134, 10.1007/978-3-642-64981-3
Huybrechts, 2003, The Brauer group for analytic K3-surfaces, Internat. Math. Res. Not., 50, 2687, 10.1155/S1073792803131637
Inoue, 1974, On surfaces of class VII0, Invent. Math., 24, 269, 10.1007/BF01425563
Iversen, 1976, Brauer group of a linear algebraic group, J. Algebra, 42, 295, 10.1016/0021-8693(76)90100-9
Iversen, 1986
Iwasawa, 1949, On some types of topological groups, Ann. Math., 50, 507, 10.2307/1969548
G. Karpilovsky, The Schur Multiplier, London Mathematical Society Monographs, vol. 2, Clarendon Press, New York, 1987.
Kato, 1975, Topology of Hopf surfaces, J. Math. Soc. Japan, 27, 222, 10.2969/jmsj/02720222
Kato, 1989, Erratum to “Topology of Hopf surfaces”, J. Math. Soc. Japan, 41, 173, 10.2969/jmsj/04110173
Kazama, 1984, ∂¯ cohomology of (H,C)-groups, Publ. Res. Inst. Math. Sci., 20, 297, 10.2977/prims/1195181609
Kodaira, 1963, On compact analytic surfaces II, Ann. Math., 77, 563, 10.2307/1970131
Kodaira, 1966, On the structure of compact complex analytic surfaces II, Amer. J. Math., 88, 682, 10.2307/2373150
Laufer, 1971, Normal two-dimensional singularities, Ann. Math. Stud., 71
Li, 1990, A simple proof of Bogomolov's theorem on class VII0 surfaces with b2=0, Illinois J. Math., 34, 217, 10.1215/ijm/1255988265
Li, 1994, On projectively flat Hermitian manifolds, Comm. Anal. Geom., 2, 103, 10.4310/CAG.1994.v2.n1.a6
Mall, 1991, The cohomology of line bundles on Hopf manifolds, Osaka J. Math., 28, 999
Maurer, 1978, Auflösung der Entartungen holomorpher Abbildungen zwischen zweidimensionalen Mannigfaltigkeiten, Math. Ann., 234, 89, 10.1007/BF01409343
Nori, 1986, On the lattice of transcendental cycles on an elliptic surface, Math. Z., 193, 105, 10.1007/BF01163358
Schneebeli, 1978, Group extensions whose profinite completion is exact, Arch. Math. (Basel), 31, 244, 10.1007/BF01226444
Schröer, 2001, There are enough Azumaya algebras on surfaces, Math. Ann., 321, 439, 10.1007/s002080100236
Schröer, 2003, The bigger Brauer group is really big, J. Algebra, 262, 210, 10.1016/S0021-8693(03)00026-7
Serre, 1955, Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier, 6, 1, 10.5802/aif.59
J.-P. Serre, Algèbre locale. Multiplicités, Lecture Notes in Mathematics, vol. 11, Springer, Berlin, 1965.
J.-P. Serre, Cohomologie galoisienne, fifth ed., Lecture Notes in Mathematics, vol. 5, Springer, Berlin, 1994.
Siu, 1969, Analytic sheaf cohomology groups of dimension n of n-dimensional complex spaces, Trans. Amer. Math. Soc., 143, 77
Teleman, 1994, Projectively flat surfaces and Bogomolov's theorem on class VII0 surfaces, Internat. J. Math., 5, 253, 10.1142/S0129167X94000152
C. Voisin, Hodge theory and complex algebraic geometry, I, Cambridge Studies in Advanced Mathematics, vol. 76, Cambridge University Press, Cambridge, 2002.
Xiao, 1991, π1 of elliptic and hyperelliptic surfaces, Internat. J. Math., 2, 599, 10.1142/S0129167X91000338