Inhalt

•  
   Introduction
•  
   Acknowledgments
•  
  Background
•  
   General setting and notation
•  
   Some notions and facts from Bruhat–Tits theory
•  
   The pro-p Iwahori subgroup
•  
  The pro-p Iwahori–Hecke algebra
•  
   Definition and Iwahori–Matsumoto presentation
•  
   Bernstein presentation
•  
   Idempotents
•  
   The pro-p Iwahori–Hecke algebra for SL_2
•  
   The centre of the pro-p Iwahori–Hecke algebra
•  
   The centre of the pro-p Iwahori–Hecke algebra for SL_2
•  
   Some results on the cohomology of pro-p groups
•  
  The Ext-algebra
•  
   Definition and description in terms of group cohomology
•  
   Shapiro isomorphism
•  
   Cup product
•  
   The product in the Ext-algebra
•  
   Anti-involution
•  
   Duality
•  
   The top graded piece
•  
   Filtrations
•  
  The Ext-algebra for SL_2
•  
   Preliminaries
•  
   The 1st graded piece E^1: elements as triples
•  
   The 1st graded piece E^1: explicit formulas
•  
   The 1st graded piece E^1: the E^0-bimodule structure
•  
   The 2nd graded piece E^2
•  
   The top graded piece E^d
•  
  The centre of the Ext-algebra for SL_2(Q_p) with p 2,3
•  
   Summary of the results
•  
   The top graded piece of the centre
•  
  Structure of top graded piece of the centre as a Z(E^0)-module
•  
   Assumptions and preliminaries
•  
   The components e_ Z(E*)^d
•  
   Final description of the structure of Z(E*)^d as a Z(E^0)-module
•  
   The 0th graded piece of the centre
•  
   The 1st graded piece of the centre
•  
   The 2nd graded piece of the centre
•  
   Computation of Z_(E^0)(E^2)
•  
   Rewrite of the basis of Z_(E^0)(E^2)
•  
   Computation of Z(E*)^2
•  
   Structure of the 2nd graded piece of the centre as a Z(E^0)-module
•  
   Multiplicative structure of Z(E*)
•  
  The Ext-algebra for more general groups: low graded pieces of the centre and other remarks
•  
  The 0th graded piece of the centre
•  
   Statement
•  
   Proofs
•  
  The 1st graded piece of the centre
•  
   Summary of the results
•  
   A first lemma about Z_(E^0)(E^1)
•  
   The 1st graded piece of the centre for unramified extensions of Q_p: partial description
•  
   Results about split tori
•  
   A result about the fundamental group
•  
   Results about the commutator subgroup of the group of rational points
•  
   The 1st graded piece of the centre for unramified extensions of Q_p: full description in the general case
•  
   Examples
•  
   A remark about a graded-commutative algebra inside E*
•  
   The 1st graded piece of the centre for unramified extensions of Q_p: special cases
•  
   A remark about the ramified case
•  
   ``Toric'' subalgebras
•  
  The Ext-algebra and the tensor algebra of E^1 for SL_2(Q_p) with p 2,3
•  
   E* is generated by E^1
•  
   Counterexample: E* is not generated by E^1 in the case G = SL_2(Q_3)
•  
   The tensor algebra
•  
   An ``algorithm'' for the computation of kernels
•  
   The kernel in degree 2
•  
   Preliminaries
•  
   Generators of T_E_0^2 E^1 as an E^0-bimodule
•  
   A section of the multiplication map in degree 2
•  
   Computation of the kernel in degree 2
•  
  The kernel in degree 3
•  
   A section of the multiplication map in degree 3
•  
   Computation of the kernel in degree 3
•  
   The kernel in degree 4
•  
   Main result
•  
   The ideal ker(M) is not generated by its 2nd graded piece
•  
   The Ext-algebra in terms of generators and relations
•  
   Bibliography