Erratum for

“Galois Algebras, Hasse Principle,

and Induction–Restriction Methods”

cf. Documenta Math. 16 (2011), 677–707

E. Bayer–Fluckiger and R. Parimala

Revised: February 17, 2013

Communicated by Ulf Rehmann

Abstract. This is a correction to [BP 11] E. Bayer–Fluckiger, R. Parimala, Galois algebras, Hasse principle and induction–restriction methods, Documenta Math. 16 (2011), 677–707.

Theorem 3.5 of [BP 11] is not correct as stated, and should be replaced by

Theorem. Let V be a k[G]–module that is a finite dimensional k–vector space, and let E = End(V). Let R_{E} be the radical of E, and set \overline{E} = E/R_{E}. Suppose that all the orthogonal components of \overline{E} are split, and let (V, q), (V, q′) be two G–forms. Then q ≃_{G} q′ over k if and only if q ≃_{G} q′ over all the completions of k.

This is proved in [BPN 13], Theorem 2.1. Note however that very few changes are needed in [BP 11]. Indeed, Theorem 3.5 and its proof are correct when k[G] is semi–simple, and this is the only case that is used in the sequel of [BP 11].

Bibliography

[BP 11] E. Bayer–Fluckiger, R. Parimala, Galois algebras, Hasse principle and induction–restriction methods, Documenta Math. 16 (2011), 677–707.

[BNP 13] E. Bayer–Fluckiger, B. Nivedita and R. Parimala, Hasse principle for G–quadratic forms, Documenta Math. 18, 383–392 (2013), Eva Bayer–Fluckiger École Polytechnique Fédérale de Lausanne EPFL/FSB/MATHGEOM/CSAG Station 8 1015 Lausanne, Switzerland eva.bayer@epfl.ch Raman Parimala Department of Mathematics & Computer Science Emory University Atlanta, GA 30322, USA. parimala@mathcs.emory.edu