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Project C2: Linear algebraic groups over arbitrary fields


Principal Investigator(s)
Investigator(s)

Summary:

The theory of semisimple linear algebraic groups is well known, up to the so-called anisotropic groups. Examples of anisotropic groups are given by the compact real Lie groups, which are relatively well known. But there are many such groups in more general situations whose properties are totally unknown. In fact it is true that all semisimple linear groups are derived by `specialization` from their `anisotropic forms`.<br /> <br /> This project proposes to develop methods in order to classify these anisotropic groups and to get informations about their internal structure. Tools are obtained from Galois cohomology, from generic splitting techniques and from the techniques which are used by the so called underlying `related structures\' of linear groups, like quadratic and Hermitean forms, Azumaya, Lie, and Jordan algebras.<br /> <br /> Conversely, knowledge about those structures can be obtained from knowledge of these groups. Linear algebraic groups and their underlying structures always have been and still are of importance in many areas of mathematics and other sciences.



Recent Preprints:

08127 Ulf Rehmann PDF

Linear Algebraic Groups and K-Theory

Project: C2

Published: Some Recent Developments in Algebraic K-theory, ICTP Publ. 23 (2008)

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Linear Algebraic Groups and K-Theory


Authors: Ulf Rehmann Projects: C2
Submission Date: 2008-12-01 Submitter: Markus Rost
Download: PDF Link: 08127
Published: Some Recent Developments in Algebraic K-theory, ICTP Publ. 23 (2008)

08126 Ahmed Laghribi, Ulf Rehmann PDF

On bilinear forms of height 2 and degree 1 or 2 in characteristic 2

Project: C2

To appear: J. Alg. (0)

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On bilinear forms of height 2 and degree 1 or 2 in characteristic 2


Authors: Ahmed Laghribi, Ulf Rehmann Projects: C2
Submission Date: 2008-12-01 Submitter: Markus Rost
Download: PDF Link: 08126
To appear: J. Alg. (0)

08125 Ulf Rehmann, Sergey Tikhonov, Vyacheslav Yanchevskii PDF

Symbols and cyclicity of algebras after a scalar extension

Project: C2

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Symbols and cyclicity of algebras after a scalar extension


Authors: Ulf Rehmann, Sergey Tikhonov, Vyacheslav Yanchevskii Projects: C2
Submission Date: 2008-12-01 Submitter: Markus Rost
Download: PDF Link: 08125

08122 Markus Rost PDF

On the basic correspondance of a splitting variety

Project: C2

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On the basic correspondance of a splitting variety


Authors: Markus Rost Projects: C2
Submission Date: 2008-12-01 Submitter: Ulf Rehmann
Download: PDF Link: 08122

08054 Gopal Prasad, Andrei Rapinchuk PDF

Local-global principles for embedding of fields with involution into simple algebras with involution

Project: B1, C2

Published: Comment. Math. Helv. 85, no. 3 (2010), 583-645

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Local-global principles for embedding of fields with involution into simple algebras with involution


Authors: Gopal Prasad, Andrei Rapinchuk Projects: B1, C2
Submission Date: 2008-06-25 Submitter: Herbert Abels
Download: PDF Link: 08054
Published: Comment. Math. Helv. 85, no. 3 (2010), 583-645

08033 Ivan Panin, Kirill Zainoulline PDF

Gersten resolutions with supports

Project: C2

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Gersten resolutions with supports


Authors: Ivan Panin, Kirill Zainoulline Projects: C2
Submission Date: 2008-05-06 Submitter: Ulf Rehmann
Download: PDF Link: 08033

06050 Michael Baake, Peter A. B. Pleasants, Ulf Rehmann PDF

Coincidence site modules in 3-space

Project: B2, C2

Published: Discr. Comput. Geom. 38 (2007), 111-138

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Coincidence site modules in 3-space


Authors: Michael Baake, Peter A. B. Pleasants, Ulf Rehmann Projects: B2, C2
Submission Date: 2006-10-16 Submitter: Michael Baake
Download: PDF Link: 06050
Published: Discr. Comput. Geom. 38 (2007), 111-138

06049 Alexander Vishik, Kirill Zainoulline PDF

Motivic splitting lemma

Project: C2

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Motivic splitting lemma


Authors: Alexander Vishik, Kirill Zainoulline Projects: C2
Submission Date: 2006-11-10 Submitter:
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Download: PDF Link: 06049



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