Formal loops II : a local Riemann-Roch theorem for determinantal gerbes
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 40 (2007) no. 1, pp. 113-133.
@article{ASENS_2007_4_40_1_113_0,
     author = {Kapranov, Mikhail and Vasserot, \'Eric},
     title = {Formal loops {II} : a local {Riemann-Roch} theorem for determinantal gerbes},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {113--133},
     publisher = {Elsevier},
     volume = {Ser. 4, 40},
     number = {1},
     year = {2007},
     doi = {10.1016/j.ansens.2006.12.003},
     zbl = {1129.14022},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.ansens.2006.12.003/}
}
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
SP  - 113
EP  - 133
VL  - 40
IS  - 1
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.ansens.2006.12.003/
DO  - 10.1016/j.ansens.2006.12.003
LA  - en
ID  - ASENS_2007_4_40_1_113_0
ER  - 
%0 Journal Article
%A Kapranov, Mikhail
%A Vasserot, Éric
%T Formal loops II : a local Riemann-Roch theorem for determinantal gerbes
%J Annales scientifiques de l'École Normale Supérieure
%D 2007
%P 113-133
%V 40
%N 1
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.ansens.2006.12.003/
%R 10.1016/j.ansens.2006.12.003
%G en
%F ASENS_2007_4_40_1_113_0
Kapranov, Mikhail; Vasserot, Éric. Formal loops II : a local Riemann-Roch theorem for determinantal gerbes. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 40 (2007) no. 1, pp. 113-133. doi : 10.1016/j.ansens.2006.12.003. http://archive.numdam.org/articles/10.1016/j.ansens.2006.12.003/

[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. | MR | Zbl

[2] Anderson G., Pablos Romo F., Simple proofs of classical explicit reciprocity laws on curves using determinantal groupoids over an artinian local ring, Comm. Algebra 32 (2004) 79-102. | MR | Zbl

[3] Bloch S., K 2 and algebraic cycles, Ann. of Math. 99 (1974) 349-379. | MR | Zbl

[4] Bressler P., Kapranov M., Tsygan B., Vasserot É., Riemann-Roch for real varieties, in preparation.

[5] Bosch S., Lütkebohmert W., Raynaud M., Néron Models, Springer-Verlag, Berlin/New York, 1990. | MR | Zbl

[6] Breen L., On the classification of 2-gerbes and 2-stacks, Astérisque 225 (1994). | Numdam | MR | Zbl

[7] Brylinski J.-L., Deligne P., Central extensions of reductive groups by K 2 , Publ. Math. IHÉS 94 (2001) 5-85. | Numdam | MR | Zbl

[8] Contou-Carrère C., Jacobienne locale, groupe de bivecteurs de Witt universel et symbole modéré, C. R. Acad. Sci. Paris, Série I 318 (1994) 743-746. | MR | Zbl

[9] Deligne P., Le déterminant de la cohomologie, Contemp. Math. 67 (1987) 93-177. | MR | Zbl

[10] Deligne P., Le symbole modéré, Publ. Math. IHÉS 73 (1991) 147-181. | Numdam | MR | Zbl

[11] Drinfeld V., Infinite-dimensional vector bundles in algebraic geometry (an introduction), math.AG/0309155.

[12] Elbaz-Vincent Ph., Mueller-Stach S., Milnor K-theory of rings, higher Chow groups and applications, Invent. Math. 148 (2002) 177-206. | MR | Zbl

[13] Gillet H., Riemann-Roch theorems for higher algebraic K-theory, Adv. Math. 40 (1981) 203-289.

[14] Goncharov A.B., Explicit construction of characteristic classes, in: Adv. Soviet Math., vol. 16, Amer. Math. Soc., Providence, RI, 1993, pp. 169-210. | MR | Zbl

[15] Denef J., Loeser F., Germs of arcs on singular algebraic varieties and motivic integration, Invent. Math. 135 (1999) 201-232. | MR | Zbl

[16] Gorbounov V., Malikov F., Schechtman V., Gerbes of chiral differential operators, Math. Res. Lett. 7 (2000) 55-66. | MR | Zbl

[17] Gorbounov V., Malikov F., Schechtman V., Gerbes of chiral differential operators. II. Vertex algebroids, Invent. Math. 155 (2004) 605-680. | MR | Zbl

[18] Haboush W., Infinite-dimensional algebraic geometry: algebraic structures on p-adic groups and their homogeneous spaces, Tohoku Math. J. 57 (2005) 65-117. | MR | Zbl

[19] Kac V., Vertex Algebras for Beginners, University Lecture Series, vol. 10, Amer. Math. Soc., Providence, RI, 1996. | MR | Zbl

[20] Kapranov M., Vasserot É., Vertex algebras and the formal loop space, Publ. Math. IHÉS 100 (2004) 209-269. | Numdam | MR | Zbl

[21] Kapranov M., Vasserot É., Formal loops III: Chiral differential operators, in preparation.

[22] Kumar S., Kac-Moody Groups, Their Flag Varieties and Representation Theory, Progress in Math., vol. 204, Birkhäuser, Basel, 2002. | Zbl

[23] Laumon G., Moret-Bailly L., Champs algébriques, A Series of Modern Surveys in Mathematics, vol. 39, Springer-Verlag, Berlin/New York, 2000. | MR

[24] Matsumoto H., Sur les sous-groupes arithmétiques des groupes semi-simples déployés, Ann. Sci. École Norm. Sup. 2 (1969) 1-62. | Numdam | MR | Zbl

[25] Moore C.C., Group extensions of p-adic and adelic linear groups, Publ. Math. IHÉS 35 (1968) 157-222. | Numdam | MR | Zbl

[26] Malikov F., Schechtman V., Vaintrob A., Chiral de Rham complex, Comm. Math. Phys. 204 (1999) 439-473. | MR | Zbl

[27] Pressley A., Segal G., Loop Groups, Oxford Univ. Press, London, 1986. | MR | Zbl

[28] Srinivas V., Algebraic K-theory, Birkhäuser, Basel, 1996. | MR | Zbl

[29] Van Der Kallen W., The K 2 of rings with many units, Ann. Sci. École Norm. Sup. 10 (1977) 473-515. | Numdam | MR | Zbl

Cité par Sources :