Abstract
This article is concerned with developing a formalism for complexes of ℓ-adic sheaves instead of just for the sheaves themselves as was done in [SGA5:Exp.V]. The need for such a generalisation has become apparent from the theory of perverse sheaves, which by their definition are complexes of ℓ-adic sheaves. When trying to carry through such an extension one is immediately faced with two problems. On the one hand it is clear already from the case of ℓ-adic sheaves that — contrary to the case of torsion sheaves — one is not dealing with actual sheaves but rather inverse systems of sheaves. On the other hand one wants to pretend that one is dealing with sheaves and not some more abstract objects.
To Alexandre Grothendieck on his 60th birthday
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
A. A. Beilinson, J. Bernstein, P. Deligne, “Faisceaux pervers”, Astérisque 100 (1983), 1–172.
P. Deligne, “La conjecture de Weil. II”, Publ. Math. 52 (1980), 137–252.
T. Ekedahl, “On the multiplicative properties of the deRham-Witt complex. II”, Arkiv för matematik 23 (1985), 53–102.
L. Illusie, “Complexe cotangent et déformations II, SLN 283, Springer-Verlag.
M. Artin, A. Grothendieck, J.-L. Verdier, “Séminaire de géométrie algébrique du Bois-Marie 1963/64, Théorie des topos et cohomologie étale des schémas, SGA 4, SLN 269, 270, 365, Springer-Verlag.
A. Grothendieck, “Séminaire de géométrie algébrique du Bois-Marie 1965–66, Cohomologie ℓ-adique et fonctions L, SGA5, SLN 589, Springer-Verlag.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Birkhäuser Boston
About this chapter
Cite this chapter
Ekedahl, T. (2007). On The Adic Formalism. In: Cartier, P., Katz, N.M., Manin, Y.I., Illusie, L., Laumon, G., Ribet, K.A. (eds) The Grothendieck Festschrift. Modern Birkhäuser Classics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4575-5_4
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4575-5_4
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-4567-0
Online ISBN: 978-0-8176-4575-5
eBook Packages: Springer Book Archive