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
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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
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- 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
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