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The Grayson spectral sequence for hermitian Ktheory
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Markett, Simon A. (2015) The Grayson spectral sequence for hermitian Ktheory. PhD thesis, University of Warwick.

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Official URL: http://webcat.warwick.ac.uk/record=b2846019~S1
Abstract
Let R be a regular ring such that 2 is invertible. We construct a spectral sequence converging to the hermitian Ktheory, alias the GrothendieckWitt theory, of R. In particular, we construct a tower for the hermitian Kgroups in even shifts, whose terms are given by the hermitian Ktheory of automorphisms. The spectral sequence arises as the homotopy spectral sequence of this tower and is analogous to Grayson’s version of the motivic spectral sequence [Gra95].
Further, we construct similar towers for the hermitian Ktheory in odd shifts if R is a field of characteristic different from 2. We show by a counter example that the arising spectral sequence does not behave as desired. We proceed by proposing an alternative version for the tower and verify its correctness in weight 1. Finally we give a geometric representation of the (hermitian) Ktheory of automorphisms in terms of the general linear group, the orthogonal group, or in terms of esymmetric matrices, respectively.
The Ktheory of automorphisms can be identified with motivic cohomology if R is local and of finite type over a field. Therefore the hermitian Ktheory of automorphisms as presented in this thesis is a candidate for the analogue of motivic cohomology in the hermitian world.
Item Type:  Thesis (PhD)  

Subjects:  Q Science > QA Mathematics  
Library of Congress Subject Headings (LCSH):  Spectral sequences (Mathematics), Ktheory  
Official Date:  February 2015  
Dates: 


Institution:  University of Warwick  
Theses Department:  Mathematics Institute  
Thesis Type:  PhD  
Publication Status:  Unpublished  
Supervisor(s)/Advisor:  Schlichting, Marco  
Extent:  vii, 126 leaves : charts  
Language:  eng 
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