Adjoint groups over ℚ_{𝕡}(𝕏) and R-equivalence - revisited

DOI10.1090/proc/13304zbMath1396.20048OpenAlexW2963946546MaRDI QIDQ3181312

Abhay Soman, Raman Preeti

Publication date: 29 December 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/13304

Mathematics Subject Classification ID

Rational points (14G05) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Other nonalgebraically closed ground fields in algebraic geometry (14G27) Bilinear and Hermitian forms (11E39) Finite-dimensional division rings (16K20) Classical groups (11E57) Linear algebraic groups over local fields and their integers (20G25) Galois cohomology of linear algebraic groups (11E72) Algebraic functions and function fields in algebraic geometry (14H05)

Cites Work

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• The \(u\)-invariant of the function fields of \(p\)-adic curves
• Cohomological invariants and \(R\)-triviality of adjoint classical groups.
• Invarianten hermitescher Formen über Schiefkörpern. (Invariant Hermitean forms over skew fields)
• Classical groups and the Hasse principle.
• Galois Cohomology
• Examples of non-rational varieties of adjoint groups
• \(R\)-equivalence and rationality problem for semisimple adjoint classical algebraic groups
• Hasse principle for classical groups over function fields of curves over number fields
• Isotropy of quadratic forms over function fields of \(p\)-adic curves
• Galois cohomology of the classical groups over fields of cohomological dimension \(\leq 2\)
• Adjoint groups over \(\mathbb Q_p(X)\) and R-equivalence.
• Classification theorems for Hermitian forms, the Rost kernel and Hasse principle over fields with \(\mathrm{cd}_2(k)\leq 3\)
• The multipliers of similitudes and the Brauer group of homogeneous varieties.

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