Formal loops II : a local Riemann–Roch theorem for determinantal gerbes

Mikhail Kapranov; Éric Vasserot

Annales scientifiques de l'École Normale Supérieure (2007)

  • Volume: 40, Issue: 1, page 113-133
  • ISSN: 0012-9593

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Kapranov, Mikhail, and Vasserot, Éric. "Formal loops II : a local Riemann–Roch theorem for determinantal gerbes." Annales scientifiques de l'École Normale Supérieure 40.1 (2007): 113-133. <http://eudml.org/doc/82706>.

@article{Kapranov2007,
author = {Kapranov, Mikhail, Vasserot, Éric},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {gerbes; chiral differential operators; loop spaces; Riemann-Roch theorem},
language = {eng},
number = {1},
pages = {113-133},
publisher = {Elsevier},
title = {Formal loops II : a local Riemann–Roch theorem for determinantal gerbes},
url = {http://eudml.org/doc/82706},
volume = {40},
year = {2007},
}

TY - JOUR
AU - Kapranov, Mikhail
AU - Vasserot, Éric
TI - Formal loops II : a local Riemann–Roch theorem for determinantal gerbes
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2007
PB - Elsevier
VL - 40
IS - 1
SP - 113
EP - 133
LA - eng
KW - gerbes; chiral differential operators; loop spaces; Riemann-Roch theorem
UR - http://eudml.org/doc/82706
ER -

References

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  1. [1] Arbarello E., De Concini C., Kac V., The infinite wedge representation and the reciprocity law for algebraic curves, Part 1, in: Proc. Sympos. Pure Math., vol. 49, Amer. Math. Soc., Providence, RI, 1989, pp. 171-190. Zbl0699.22028MR1013132
  2. [2] Anderson G., Pablos Romo F., Simple proofs of classical explicit reciprocity laws on curves using determinantal groupoids over an artinian local ring, Comm. Algebra32 (2004) 79-102. Zbl1077.14033MR2036223
  3. [3] Bloch S., K 2 and algebraic cycles, Ann. of Math.99 (1974) 349-379. Zbl0298.14005MR342514
  4. [4] Bressler P., Kapranov M., Tsygan B., Vasserot É., Riemann–Roch for real varieties, in preparation. Zbl1230.14010
  5. [5] Bosch S., Lütkebohmert W., Raynaud M., Néron Models, Springer-Verlag, Berlin/New York, 1990. Zbl0705.14001MR1045822
  6. [6] Breen L., On the classification of 2-gerbes and 2-stacks, Astérisque225 (1994). Zbl0818.18005MR1301844
  7. [7] Brylinski J.-L., Deligne P., Central extensions of reductive groups by K 2 , Publ. Math. IHÉS94 (2001) 5-85. Zbl1093.20027MR1896177
  8. [8] Contou-Carrère C., Jacobienne locale, groupe de bivecteurs de Witt universel et symbole modéré, C. R. Acad. Sci. Paris, Série I318 (1994) 743-746. Zbl0840.14031MR1272340
  9. [9] Deligne P., Le déterminant de la cohomologie, Contemp. Math.67 (1987) 93-177. Zbl0629.14008MR902592
  10. [10] Deligne P., Le symbole modéré, Publ. Math. IHÉS73 (1991) 147-181. Zbl0749.14011MR1114212
  11. [11] Drinfeld V., Infinite-dimensional vector bundles in algebraic geometry (an introduction), math.AG/0309155. Zbl1108.14012
  12. [12] Elbaz-Vincent Ph., Mueller-Stach S., Milnor K-theory of rings, higher Chow groups and applications, Invent. Math.148 (2002) 177-206. Zbl1027.19004MR1892848
  13. [13] Gillet H., Riemann–Roch theorems for higher algebraic K-theory, Adv. Math.40 (1981) 203-289. Zbl0478.14010
  14. [14] Goncharov A.B., Explicit construction of characteristic classes, in: Adv. Soviet Math., vol. 16, Amer. Math. Soc., Providence, RI, 1993, pp. 169-210. Zbl0809.57016MR1237830
  15. [15] Denef J., Loeser F., Germs of arcs on singular algebraic varieties and motivic integration, Invent. Math.135 (1999) 201-232. Zbl0928.14004MR1664700
  16. [16] Gorbounov V., Malikov F., Schechtman V., Gerbes of chiral differential operators, Math. Res. Lett.7 (2000) 55-66. Zbl0982.17013MR1748287
  17. [17] Gorbounov V., Malikov F., Schechtman V., Gerbes of chiral differential operators. II. Vertex algebroids, Invent. Math.155 (2004) 605-680. Zbl1056.17022MR2038198
  18. [18] Haboush W., Infinite-dimensional algebraic geometry: algebraic structures on p-adic groups and their homogeneous spaces, Tohoku Math. J.57 (2005) 65-117. Zbl1119.14004MR2113991
  19. [19] Kac V., Vertex Algebras for Beginners, University Lecture Series, vol. 10, Amer. Math. Soc., Providence, RI, 1996. Zbl0861.17017MR1417941
  20. [20] Kapranov M., Vasserot É., Vertex algebras and the formal loop space, Publ. Math. IHÉS100 (2004) 209-269. Zbl1106.17038MR2102701
  21. [21] Kapranov M., Vasserot É., Formal loops III: Chiral differential operators, in preparation. Zbl1154.14007
  22. [22] Kumar S., Kac–Moody Groups, Their Flag Varieties and Representation Theory, Progress in Math., vol. 204, Birkhäuser, Basel, 2002. Zbl1026.17030
  23. [23] Laumon G., Moret-Bailly L., Champs algébriques, A Series of Modern Surveys in Mathematics, vol. 39, Springer-Verlag, Berlin/New York, 2000. MR1771927
  24. [24] Matsumoto H., Sur les sous-groupes arithmétiques des groupes semi-simples déployés, Ann. Sci. École Norm. Sup.2 (1969) 1-62. Zbl0261.20025MR240214
  25. [25] Moore C.C., Group extensions of p-adic and adelic linear groups, Publ. Math. IHÉS35 (1968) 157-222. Zbl0159.03203MR244258
  26. [26] Malikov F., Schechtman V., Vaintrob A., Chiral de Rham complex, Comm. Math. Phys.204 (1999) 439-473. Zbl0952.14013MR1704283
  27. [27] Pressley A., Segal G., Loop Groups, Oxford Univ. Press, London, 1986. Zbl0618.22011MR900587
  28. [28] Srinivas V., Algebraic K-theory, Birkhäuser, Basel, 1996. Zbl0860.19001MR1382659
  29. [29] van der Kallen W., The K 2 of rings with many units, Ann. Sci. École Norm. Sup.10 (1977) 473-515. Zbl0393.18012MR506170

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