Commentarii Mathematici Helvetici


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Volume 86, Issue 2, 2011, pp. 437–468
DOI: 10.4171/CMH/230

Published online: 2011-02-27

Push-forwards for Witt groups of schemes

Baptiste Calmès[1] and Jens Hornbostel[2]

(1) Université d'Artois, Lens, France
(2) Bergische Universität Wuppertal, Germany

Using suitable closed symmetric monoidal structures on derived categories of schemes, as well as adjunctions of the type $({\rm L}f^*,{\rm R}f_*)$ and $({\rm R}f_*,f^!)$ (i.e. Grothendieck duality theory), we define push-forwards for coherent Witt groups along proper morphisms between separated noetherian schemes. We also establish fundamental theorems for these push-forwards (e.g. base change and projection formula) and provide some computations.

Keywords: Witt groups of schemes, push-forward, transfer, Grothendieck duality, quadratic forms

Calmès Baptiste, Hornbostel Jens: Push-forwards for Witt groups of schemes. Comment. Math. Helv. 86 (2011), 437-468. doi: 10.4171/CMH/230