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On the trace form of Galois algebras
Author(s) -
CassouNoguès Philippe,
Chinburg Ted,
Morin Baptiste,
Taylor Martin J.
Publication year - 2018
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms.12193
Subject(s) - mathematics , galois group , galois cohomology , pure mathematics , fundamental theorem of galois theory , embedding problem , trace (psycholinguistics) , galois module , invariant (physics) , differential galois theory , algebra over a field , discrete mathematics , linguistics , philosophy , mathematical physics
We study the trace form q L of G ‐Galois algebras L / K when G is a finite group and K is a field of characteristic different from 2. We introduce in this paper the category of 2‐reduced groups and, when G is such a group, we use a formula of Serre to compute the second Hasse–Witt invariant of q L . By combining this computation with work of Quillen we determine the isometry class of q L for large families of G ‐Galois algebras over global fields. We also indicate how our results generalize to Galois G ‐covers of schemes.