Three notes on real analytic groups

Math 535: Real Groups Lecture Notes

Notes on Classical Groups

These notes are the content of an M.Sc. course I gave at Queen Mary and Westfield College, London, in January–March 2000. I am grateful to the students on the course for their comments; to Keldon Drudge, for standing in for me; and to Simeon Ball, for helpful discussions.

Notes on Cyclic Groups

is a (abelian) subgroup of G. From this point on we will use the exponent laws without particular reference. The group G is cyclic if G = for some a ∈ G in which case a is said to generate G. Since = for all a ∈ G, if G is cyclic and generated by a then G is also generated by a−1. Suppose that the binary operation of G is written additively. Then the notation n·a, or na, is used i...

Lecture Notes on Lie Groups

SOME NOTES ON COHOMOLOGY OF NUMBER FIELDS AND ANALYTIC PRO-p-GROUPS by

In this paper, we are interested in the tame version of the Fontaine-Mazur conjecture. After recalling the role of étale cohomology in the context of this conjecture, we establish a relationship between it and the computation of the cohomological dimension of the pro-p-groups GS that appear. We then look at this conjecture by viewing the pro-pproup GS as a quotient of a Galois group with rami c...