By Mikhail Borovoi

During this quantity, a brand new functor $H^2_{ab}(K,G)$ of abelian Galois cohomology is brought from the class of attached reductive teams $G$ over a box $K$ of attribute $0$ to the class of abelian teams. The abelian Galois cohomology and the abelianization map$ab^1:H^1(K,G) \rightarrow H^2_{ab}(K,G)$ are used to offer a functorial, nearly particular description of the standard Galois cohomology set $H^1(K,G)$ while $K$ is a bunch box.

Show description

Read or Download Abelian Galois cohomology of reductive groups PDF

Best linear books

Geometric linear algebra

This obtainable booklet for novices makes use of intuitive geometric suggestions to create summary algebraic conception with a different emphasis on geometric characterizations. The ebook applies identified effects to explain a number of geometries and their invariants, and provides difficulties keen on linear algebra, resembling in actual and complicated research, differential equations, differentiable manifolds, differential geometry, Markov chains and transformation teams.

Representation Theory and Analysis on Homogeneous Spaces: A Conference in Memory of Larry Corwin February 5-7, 1993 Rutgers University

Combining presentation of latest effects with in-depth surveys of contemporary paintings, this publication makes a speciality of illustration concept and harmonic research on genuine and $p$-adic teams. The papers are in line with lectures awarded at a convention devoted to the reminiscence of Larry Corwin and held at Rutgers collage in February 1993.

Mathematical Tapas Volume 1 (for Undergraduates)

This booklet incorporates a choice of routines (called “tapas”) at undergraduate point, usually from the fields of genuine research, calculus, matrices, convexity, and optimization. lots of the difficulties awarded listed here are non-standard and a few require vast wisdom of alternative mathematical topics so that it will be solved.

Extra info for Abelian Galois cohomology of reductive groups

Sample text

Borovoi, On strong approximation for homogeneous spaces, Dokl. Akad. Nauk BSSR 33 (1989) N4, 293–296 (Russian). [Brv3] M. V. Borovoi, On weak approximation in homogeneous spaces of algebraic groups, Soviet Math. Dokl. 42 (1991), 247–251. [Brv4] M. V. Borovoi, On weak approximation in homogeneous spaces of simply connected algebraic groups, Proc. Internat. Conf. “Automorphic Functions and Their Applications, Khabarovsk, June 27 – July 4, 1988” (N. Kuznetsov, V. ), Khabarovsk, 1990, 64–81. [Brv5] M.

7. Let G be a connected reductive group over a number field K. Then 1 the map ab1 : H 1 (K, G) → Hab (K, G) is surjective. 1 Proof: Let h ∈ Hab (K, G). It suffices to construct a torus T ⊂ G such that the 1 1 image of H (K, T ) in H1 (K, T (sc) → T ) = Hab (K, G) contains h. 6 there exists a finite set S of places of K such that locv (h) = 0 for v ∈ / S. 5. We set T = ρ(T (sc) ) · Z(G)0 ; then T (sc) = T . 2) δ 1 · · · → H 1 (K, T ) → Hab (K, G)−→H 2 (K, T (sc) ) → · · · Set η = δ(h); then locv (η) = 0 for v ∈ / S.

C. , Acad. Press, London, 1967, pp. 94–115. [Bo] A. Borel, Automorphic L-functions, Automorphic forms, Representations, and L-functions, Proc. Sympos. Pure Math 33, AMS, Providence, RI, Part 2, pp. 27–61. [Brn] L. Breen, Bitorseurs et cohomologie non ab´elienne, The Grothendieck Festschrift, Birkha¨ user, Boston, 1990, vol. 1, pp. 401–476. [Br-H] R. Brown and P. Huebschmann, Identities among relations, Low-Dimensional Topology, London Math. Soc. Lecture Notes Series 48, Cambridge University Press, 1982, pp.

Download PDF sample

Rated 4.40 of 5 – based on 48 votes