Cohomological Invariants in Galois Cohomology

By Skip Garibaldi, Alexander S. Merkurjev, Jean-Pierre Serre. 2003

359 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a3a3083dd48ec29d32f41c7c3ddad236e8c45b82

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In Algebra and Number Theory

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Citations in the corpus

The Algebraic and Geometric Theory of Quadratic Forms (2008, neutral): “[46]): If m is not divisible by charF we set H(F,Z/mZ) = H ( F, μ⊗i m ) , where μ⊗i m is the ith tensor power of μm if i ≥ 0 and μ⊗i m = Hom(μ⊗−i m ,Z/mZ) if i < 0.”
Isotriviality and étale cohomology of Laurent polynomial rings (2008, background): “Since Gal(Fn) = lim ←−d Gal(Fn,d/Fn) (as one can see by induction on n, the case n = 1 being covered in [17] II.”
The torsion index of the spin groups (2005, background): “The proof produces an explicit GF-torsor E with n(E) = t(G): the natural torsor over the function field F of GL(n)/Gk, for any embedding of Gk into GL(n) over k. It follows that any versal torsor E has n(E) = t(G); a reference for the notion of versal torsors is Garibaldi-Merkurjev-Serre ([ 9 ], sec”
Essential dimension: a survey (2013, background): “Case p = 2: All lower bounds are listed in [16] or given by the Rost invariant (see [26]).”
Cohomological Invariants: Exceptional Groups and Spin Groups (2009, methodology): “We assume some familiarity with the notes from Serre’s lectures from [ GMS03 ], which we refer to hereafter as S.a A reader seeking a more leisurely introduction to the notion of invariants should”
Open problems on central simple algebras (2010, background): “Once one is interested in central simple F -algebras of degree n—equivalently, elements of H1pF,PGLnq—it is natural to want to know the invariants of PGLn in the sense of [GMS03] with values in, say, mod-2 Galois cohomology Hip ,Z{2Zq or the Witt ring W p q.”
Essential dimension: A functorial point of view (after A. Merkurjev) (2003, background): “In Section 6, we introduce the notion of generic torsor, following [9].”
Essential dimension, spinor groups and quadratic forms (2009, background): “Let E be a versal torsor for Spinn over a field extension L/k; cf. [ GMS03 , Section I.V].”
Galois cohomology and forms of algebras over Laurent polynomial rings (2007, neutral): “where �� (−1) stands for the Tate twist �� (−1) = Hom(b Z,�� ) ≃ Hom(�� d,�� ) for some d >> 0 (see [ GMS ] §I.7.8).”