Volume 12, issue 1 (2012)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 21
Issue 4, 1595–2140
Issue 3, 1075–1593
Issue 2, 543–1074
Issue 1, 1–541

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
Characteristic classes of proalgebraic varieties and motivic measures

Shoji Yokura

Algebraic & Geometric Topology 12 (2012) 601–641
1 P Aluffi, Chern classes of birational varieties, Int. Math. Res. Not. 2004 (2004) 3367 MR2098642
2 P Aluffi, Modification systems and integration in their Chow groups, Selecta Math. 11 (2005) 155 MR2183846
3 M Artin, B Mazur, Etale homotopy, 100, Springer (1969) MR0245577
4 M F Atiyah, The signature of fibre-bundles, from: "Global Analysis (Papers in Honor of K Kodaira)" (editors D C Spencer, S Iyanaga), Univ. Tokyo Press (1969) 73 MR0254864
5 J Ax, Injective endomorphisms of varieties and schemes, Pacific J. Math. 31 (1969) 1 MR0251036
6 P Baum, W Fulton, R MacPherson, Riemann–Roch for singular varieties, Inst. Hautes Études Sci. Publ. Math. (1975) 101 MR0412190
7 F Bittner, The universal Euler characteristic for varieties of characteristic zero, Compos. Math. 140 (2004) 1011 MR2059227
8 K Borsuk, Theory of shape, 28, Matematisk Institut, Aarhus Universitet (1971) 145 MR0293602
9 S Bouc, Green functors and G–sets, 1671, Springer (1997) MR1483069
10 J P Brasselet, Existence des classes de Chern en théorie bivariante, from: "Analysis and topology on singular spaces, II, III (Luminy, 1981)", Astérisque 101, Soc. Math. France (1983) 7 MR737926
11 J P Brasselet, J Schürmann, S Yokura, Classes de Hirzebruch et classes de Chern motiviques, C. R. Math. Acad. Sci. Paris 342 (2006) 325 MR2201957
12 J P Brasselet, J Schürmann, S Yokura, On Grothendieck transformations in Fulton–MacPherson’s bivariant theory, J. Pure Appl. Algebra 211 (2007) 665 MR2344222
13 J P Brasselet, J Schürmann, S Yokura, On the uniqueness of bivariant Chern class and bivariant Riemann–Roch transformations, Adv. Math. 210 (2007) 797 MR2303240
14 J P Brasselet, J Schürmann, S Yokura, Hirzebruch classes and motivic Chern classes for singular spaces, J. Topol. Anal. 2 (2010) 1 MR2646988
15 J P Brasselet, M H Schwartz, Sur les classes de Chern d’un ensemble analytique complexe, from: "The Euler–Poincaré characteristic", Astérisque 82, Soc. Math. France (1981) 93 MR629125
16 S E Cappell, A Libgober, L G Maxim, J L Shaneson, Hodge genera of algebraic varieties, II, Math. Ann. 345 (2009) 925 MR2545873
17 S E Cappell, L Maxim, J Schürmann, J L Shaneson, Equivariant characteristic classes of complex algebraic varieties, to appear in Comm. Pure Appl. Math. arXiv:1004.1844
18 S E Cappell, L Maxim, J Schürmann, J L Shaneson, Characteristic classes of complex hypersurfaces, Adv. Math. 225 (2010) 2616 MR2680178
19 S E Cappell, L Maxim, J Schürmann, J L Shaneson, S Yokura, Characteristic classes of symmetric products of complex quasi-projective varieties arXiv:1008.4299
20 S E Cappell, L Maxim, J L Shaneson, Hodge genera of algebraic varieties I, Comm. Pure Appl. Math. 61 (2008) 422 MR2376848
21 S E Cappell, J L Shaneson, Stratifiable maps and topological invariants, J. Amer. Math. Soc. 4 (1991) 521 MR1102578
22 S S Chern, F Hirzebruch, J P Serre, On the index of a fibered manifold, Proc. Amer. Math. Soc. 8 (1957) 587 MR0087943
23 A Craw, An introduction to motivic integration, from: "Strings and geometry" (editors M Douglas, J Gauntlett, M Gross), Clay Math. Proc. 3, Amer. Math. Soc. (2004) 203 MR2103724
24 J Denef, F Loeser, Germs of arcs on singular algebraic varieties and motivic integration, Invent. Math. 135 (1999) 201 MR1664700
25 J Denef, F Loeser, Geometry on arc spaces of algebraic varieties, from: "European Congress of Mathematics, Vol. I (Barcelona, 2000)" (editors C Casacuberta, R M Miró-Roig, J Verdera, S Xambó-Descamps), Progr. Math. 201, Birkhäuser (2001) 327 MR1905328
26 A W M Dress, Notes on the theory of representations of finite groups. Part I : The Burnside ring of a finite group and some AGN-applications, Universität Bielefeld, Fakultät für Mathematik (1971) MR0360771
27 A W M Dress, Contributions to the theory of induced representations, from: "Algebraic K–theory, II : “Classical” algebraic K–theory and connections with arithmetic (Proc. Conf., Battelle Memorial Inst., Seattle, WA, 1972)" (editor H Bass), Lecture Notes in Math. 342, Springer (1973) 183 MR0384917
28 D A Edwards, Étale homotopy theory and shape, from: "Algebraic and geometrical methods in topology (Conf. Topological Methods in Algebraic Topology, State Univ. New York, Binghamton, NY, 1973)" (editor L F McAuley), Lecture Notes in Math. 428, Springer (1974) 58 MR0375295
29 L Ernström, S Yokura, Bivariant Chern–Schwartz–MacPherson classes with values in Chow groups, Selecta Math. 8 (2002) 1 MR1890193
30 L Ernström, S Yokura, Addendum to : “Bivariant Chern–Schwartz–MacPherson classes with values in Chow groups” Ernstrom-Yokura1, Selecta Math. 10 (2004) 29 MR2061221
31 R H Fox, On shape, Fund. Math. 74 (1972) 47 MR0296914
32 J H G Fu, C McCrory, Stiefel–Whitney classes and the conormal cycle of a singular variety, Trans. Amer. Math. Soc. 349 (1997) 809 MR1401519
33 W Fulton, Intersection theory, 2, Springer (1984) MR732620
34 W Fulton, R MacPherson, Categorical framework for the study of singular spaces, 31, no. 243, Amer. Math. Soc. (1981) MR609831
35 E Getzler, Resolving mixed Hodge modules on configuration spaces, Duke Math. J. 96 (1999) 175 MR1663927
36 M Goresky, R MacPherson, Intersection homology theory, Topology 19 (1980) 135 MR572580
37 W Gottschalk, Some general dynamical notions, from: "Recent advances in topological dynamics (Proc. Conf. Topological Dynamics, Yale Univ., New Haven, CT, 1972 ; in honor of Gustav Arnold Hedlund)" (editor A Beck), Lecture Notes in Math. 318, Springer (1973) 120 MR0407821
38 M Gromov, Endomorphisms of symbolic algebraic varieties, J. Eur. Math. Soc. 1 (1999) 109 MR1694588
39 M Gromov, Topological invariants of dynamical systems and spaces of holomorphic maps : I, Math. Phys. Anal. Geom. 2 (1999) 323 MR1742309
40 A Grothendieck, Récoltes et semailles, réflexions et témoignages sur un passé de mathématicien (1985)
41 A Grothendieck, Technique de descente et théorèmes d’existence en géométrie algébrique, II : Le théorème d’existence en théorie formelle des modules, from: "Séminaire Bourbaki, Vol. 5", Soc. Math. France (1995) 369 MR1603480
42 F Hirzebruch, Topological methods in algebraic geometry, 131, Springer (1966) MR0202713
43 F Hirzebruch, T Berger, R Jung, Manifolds and modular forms, E20, Friedr. Vieweg & Sohn (1992) MR1189136
44 K Kodaira, A certain type of irregular algebraic surfaces, J. Analyse Math. 19 (1967) 207 MR0216521
45 M Kontsevich, Motivic integration, Lecture at Orsay (1995)
46 M Kwieciński, Formule du produit pour les classes caractéristiques de Chern–Schwartz–MacPherson et homologie d’intersection, C. R. Acad. Sci. Paris Sér. I Math. 314 (1992) 625 MR1158750
47 M Kwieciński, S Yokura, Product formula for twisted MacPherson classes, Proc. Japan Acad. Ser. A Math. Sci. 68 (1992) 167 MR1193174
48 M Levine, F Morel, Algebraic cobordism, , Springer (2007) MR2286826
49 M Levine, R Pandharipande, Algebraic cobordism revisited, Invent. Math. 176 (2009) 63 MR2485880
50 E Looijenga, Motivic measures, from: "Séminaire Bourbaki, Vol. 1999/2000", Astérisque 276 (2002) 267 MR1886763
51 R D MacPherson, Chern classes for singular algebraic varieties, Ann. of Math. 100 (1974) 423 MR0361141
52 R D MacPherson, Characteristic classes for singular varieties, from: "Proceedings of the Ninth Brazilian Mathematical Colloquium (Poços de Caldas, 1973), Vol. II (Portuguese)", Inst. Mat. Pura Apl. (1977) 321 MR534464
53 S Mardešić, J Segal, Shape theory : The inverse system approach, 26, North-Holland (1982) MR676973
54 L Maxim, M Saito, J Schürmann, Symmetric products of mixed Hodge modules, J. Math. Pures Appl. 96 (2011) 462 MR2843222
55 L Maxim, J Schürmann, Twisted genera of symmetric products, Selecta Math. 18 (2012) 283
56 T Ohmoto, Equivariant Chern classes of singular algebraic varieties with group actions, Math. Proc. Cambridge Philos. Soc. 140 (2006) 115 MR2197579
57 T Ohmoto, Generating functions of orbifold Chern classes I : Symmetric products, Math. Proc. Cambridge Philos. Soc. 144 (2008) 423 MR2405899
58 B Poonen, The Grothendieck ring of varieties is not a domain, Math. Res. Lett. 9 (2002) 493 MR1928868
59 C Sabbah, Espaces conormaux bivariants, PhD thesis, Université Paris (1986)
60 M Saito, Mixed Hodge modules, Publ. Res. Inst. Math. Sci. 26 (1990) 221 MR1047415
61 J Schürmann, A general construction of partial Grothendieck transformations arXiv:math.AG/0209299
62 J Schürmann, A generalized Verdier-type Riemann–Roch theorem for Chern–Schwartz–MacPherson classes arXiv:math.AG/0202175
63 J Schürmann, Nearby cycles and characteristic classes of singular spaces arXiv:1003.2343
64 J Schürmann, Characteristic classes of mixed Hodge modules, from: "Topology of stratified spaces" (editors G Friedman, E Hunsicker, A Libgober, L Maxim), Math. Sci. Res. Inst. Publ. 58, Cambridge Univ. Press (2011) 419 MR2796417
65 J Schürmann, S Yokura, Motivic bivariant characteristic classes arXiv:1110.2166v1
66 J Schürmann, S Yokura, A survey of characteristic classes of singular spaces, from: "Singularity theory" (editors D Chéniot, N Dutertre, C Murolo, D Trotman, A Pichon), World Sci. Publ. (2007) 865 MR2342943
67 M H Schwartz, Classes caractéristiques définies par une stratification d’une variété analytique complexe. I, C. R. Acad. Sci. Paris 260 (1965) 3262 MR0212842
68 M H Schwartz, Classes et caractères de Chern–Mather des espaces linéaires, C. R. Acad. Sci. Paris Sér. I Math. 295 (1982) 399 MR684735
69 D Sullivan, Combinatorial invariants of analytic spaces, from: "Proceedings of Liverpool Singularities—Symposium, I (1969/70)" (editor C T C Wall), Springer (1971) 165 MR0278333
70 W Veys, Arc spaces, motivic integration and stringy invariants, from: "Singularity theory and its applications" (editors S Izumiya, G Ishikawa, H Tokunaga, I Shimada, T Sano), Adv. Stud. Pure Math. 43, Math. Soc. Japan (2006) 529 MR2325153
71 J Woolf, Witt groups of sheaves on topological spaces, Comment. Math. Helv. 83 (2008) 289 MR2390046
72 S Yokura, Chern classes of proalgebraic varieties and motivic measures arXiv:math.AG/0407237
73 S Yokura, On Cappell–Shaneson’s homology L–classes of singular algebraic varieties, Trans. Amer. Math. Soc. 347 (1995) 1005 MR1283567
74 S Yokura, A singular Riemann–Roch for Hirzebruch characteristics, from: "Singularities Symposium—Łojasiewicz 70 (Kraków, 1996 ; Warsaw, 1996)" (editors B Jakubczyk, W Pawłucki, J Stasica), Banach Center Publ. 44, Polish Acad. Sci. (1998) 257 MR1677403
75 S Yokura, On a Verdier-type Riemann–Roch for Chern–Schwartz–MacPherson class, Topology Appl. 94 (1999) 315 MR1695362
76 S Yokura, On the uniqueness problem of bivariant Chern classes, Doc. Math. 7 (2002) 133 MR1911213
77 S Yokura, On Ginzburg’s bivariant Chern classes, Trans. Amer. Math. Soc. 355 (2003) 2501 MR1974000
78 S Yokura, Quasi-bivariant Chern classes obtained by resolutions of singularities, Rep. Fac. Sci. Kagoshima Univ. (2003) 17 MR2020372
79 S Yokura, Mackey functors on provarieties, from: "Real and complex singularities" (editors J P Brasselet, M A Soares Ruas), Trends Math., Birkhäuser (2007) 343 MR2280150
80 S Yokura, Motivic Milnor classes, J. Singul. 1 (2010) 39 MR2671765
81 S Yokura, Motivic characteristic classes, from: "Topology of stratified spaces" (editors G Friedman, E Hunsicker, A Libgober, L Maxim), Math. Sci. Res. Inst. Publ. 58, Cambridge Univ. Press (2011) 375 MR2796416
82 B Youssin, Witt groups of derived categories, K–Theory 11 (1997) 373 MR1451761
83 J Zhou, Classes de Chern en théorie bivariante, PhD thesis, Université Aix-Marseille (1995)
84 J Zhou, Morphisme cellulaire et classes de Chern bivariantes, Ann. Fac. Sci. Toulouse Math. 9 (2000) 161 MR1815946