Skip to main content
Log in

On injective modules over Azumaya algebras over locally noetherian schemes

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

Let \(\mathcal{A}\) be an Azumaya algebra over a locally noetherian scheme X. We describe in this work quasi-coherent \(\mathcal{A}\)-bimodules which are injective in the category of sheaves of left \(\mathcal{A}\)-modules

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bass H.: Algebraic K-theory, Benjamin (1968)

  2. Berthelot, P., Grothendieck, A., Illusie, L.: Théorie des intersections et théorème de Riemann-Roch, Séminaire de Géométrie Algébrique du Bois-Marie 1966–1967 (SGA 6). Dirigé par P. Berthelot, A. Grothendieck et L. Illusie, Springer LNM 225 (1971)

  3. Gille, S.: A Gersten-Witt complex for hermitian Witt groups of coherent algebras over schemes I: Involution of the first kind, Compos. Math. (in press) (2005)

  4. Grothendieck A. (1957) Sur quelques points d’algèbre homologique. Tohoku Math. J. 9, 119–221

    MATH  MathSciNet  Google Scholar 

  5. Grothendieck, A.: Le groupe de Brauer I: Algèbres d’Azumaya et interprétations diverses, in Dix Exposés sur la Cohomologie des Schémas, 46–66, Masson and North-Holland (1968)

  6. Hartshorne, R.: Residues and duality. Springer LNM 20 (1966)

  7. Kashiwara M., Schapira P. (2006) Categories and sheaves. Springer, Berlin Heidelberg New York

    MATH  Google Scholar 

  8. Knus, M., Ojanguren, M.: Théorie de la descente et algèbres d’Azumaya. Springer LMN 389 (1974)

  9. Matlis E. (1958) Injective modules over Noetherian rings. Pacific J. Math. 8, 511–528

    MATH  MathSciNet  Google Scholar 

  10. Orzech, M., Small, C.: The Brauer group of commutative rings. Marcel Dekker (1975)

  11. Yekutieli A. (1992) Dualizing complexes over noncommutative graded algebras. J. Algebra 153, 41–84

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Stefan Gille.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gille, S. On injective modules over Azumaya algebras over locally noetherian schemes. manuscripta math. 121, 437–450 (2006). https://doi.org/10.1007/s00229-006-0046-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00229-006-0046-2

Mathematics Subject Classification (2000)

Navigation