# On the arithmetic Chern character

Annales de la faculté des sciences de Toulouse Mathématiques (2014)

- Volume: 23, Issue: 3, page 611-619
- ISSN: 0240-2963

## Access Full Article

top## Abstract

top## How to cite

topGillet, H., and Soulé, C.. "On the arithmetic Chern character." Annales de la faculté des sciences de Toulouse Mathématiques 23.3 (2014): 611-619. <http://eudml.org/doc/275336>.

@article{Gillet2014,

abstract = {We consider a short sequence of hermitian vector bundles on some arithmetic variety. Assuming that this sequence is exact on the generic fiber we prove that the alternated sum of the arithmetic Chern characters of these bundles is the sum of two terms, namely the secondary Bott Chern class of the sequence and its Chern character with support on the finite fibers.Next, we compute these classes in the situation encountered by the second author when proving a “Kodaira vanishing theorem” for arithmetic surfaces.},

author = {Gillet, H., Soulé, C.},

journal = {Annales de la faculté des sciences de Toulouse Mathématiques},

language = {eng},

number = {3},

pages = {611-619},

publisher = {Université Paul Sabatier, Toulouse},

title = {On the arithmetic Chern character},

url = {http://eudml.org/doc/275336},

volume = {23},

year = {2014},

}

TY - JOUR

AU - Gillet, H.

AU - Soulé, C.

TI - On the arithmetic Chern character

JO - Annales de la faculté des sciences de Toulouse Mathématiques

PY - 2014

PB - Université Paul Sabatier, Toulouse

VL - 23

IS - 3

SP - 611

EP - 619

AB - We consider a short sequence of hermitian vector bundles on some arithmetic variety. Assuming that this sequence is exact on the generic fiber we prove that the alternated sum of the arithmetic Chern characters of these bundles is the sum of two terms, namely the secondary Bott Chern class of the sequence and its Chern character with support on the finite fibers.Next, we compute these classes in the situation encountered by the second author when proving a “Kodaira vanishing theorem” for arithmetic surfaces.

LA - eng

UR - http://eudml.org/doc/275336

ER -

## References

top- Bott (R.), Chern (S.S.).— Hermitian vector bundles and the equidistribution of the zeroes of their holomorphic sections. Acta Math. 114, p. 71-112 (1965). Zbl0148.31906MR185607
- Bismut (J.-M.), Gillet (H.), Soulé (C.).— Analytic torsion and holomorphic determinant bundles I, II, III. Comm. Math. Physics 115, p. 49-78, p. 79-126, p. 301-351 (1988). Zbl0651.32017MR931666
- Fulton W..— Intersection Theory. Springer 1984. Zbl0885.14002MR732620
- Gillet (H.), Soulé (C.).— Characteristic classes for algebraic vector bundles with hermitian metrics I, II. Annals of Math. 131, p. 163-203, p. 205-238 (1990). Zbl0715.14006MR1038362
- Gillet (H.), Soulé (C.).— An arithmetic Riemann-Roch theorem. Invent. Math. 110, p. 473-543 (1992). Zbl0777.14008MR1189489
- Gillet (H.), Soulé (C.).— Direct images in non-archimedean Arakelov theory. Annales de l’institut Fourier, 50, p. 363-399 (2000). Zbl0969.14015MR1775354
- Soulé (C.).— A vanishing theorem on arithmetic surfaces. Invent. Math. 116, no. 1-3, p. 577-599 (1994). Zbl0834.14013MR1253205

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.