The Class Number Formula
Version 1.022nd November, 2013 klokken 11:26.
A fundamental tool in the study of an algebraic number eld is the Dedekind Zeta
function. It is a generating function encoding a lot of the arithmetic properties of the
eld.
We x a num
Separability
MAT4250 Hst 2013
Separability
Version 1.1 24. september 2013 klokken 10:28
Multiple roots and separable polynomials
Let as usual K be a eld, and let a polynomial f 2 K[t] of degree m is given. It
is convenientand we loose nothingto suppose th
Norms and traces
MAT4250 Hst 2013
Norms and traces
Version 0.2 10. september 2013 klokken 09:55
We start by recalling a few facts from linear algebra that will be very useful for us,
and we shall do it over a general base eld K (of any characteristic). As
Geometry of numbers
MAT4250 Hst 2013
Minkowskis geometry of numbers
Preliminary version. Version
12:04
1+2 31. oktober 2013 klokken
Lattices
Let V be a real vector space of dimension n. By a lattice L in V we mean a discrete,
additive subgroup. We say tha
The discriminant
MAT4250 Hst 2013
The discriminant
First and raw version 0.1 23. september 2013 klokken 13:45
One of the most signicant invariant of an algebraic number eld is the discriminant.
One is tempted to say, apart from the degree, the most fundam
Cyclotomic fields
MAT4250 Hst 2013
Cyclotomic elds
Preliminary version. Version
10:13
1 + 22. oktober 2013 klokken
Roots of unity
The complex n-th roots of unity form a subgroup n of the multiplicative group C of
non-zero complex numbers. It is a cyclic g
Dedekind rings
MAT4250 Hst 2013
Dedekind rings
Version 3.2 27. august 2013 klokken 12:05
If not the main objects of study in algebraic number theory, Dedekind rings are the
ubiquists of the story, and it was in the surroundings of algebraic number theory
Extensions
MAT4250 Hst 2013
Extensions of Dedekind rings
Version 0.4 19. september 2013 klokken 16:13
The basic object we study in algebraic number theory are the rings of integers in
algebraic number elds. The main focus is on the prime ideals rings. The
Galois theory
MAT4250 Hst 2013
A crash course in Galois theory
First version 0.1 14. september 2013 klokken 14:50
In these notes K denotes a eld.
Embeddings
Assume that is a eld and that : K ! and embedding. If K L is an extension,
we say that the embeddi
Norms again
MAT4250 Hst 2013
First version 0.2 9. oktober 2013 klokken 16:13
Norms again
In xxx we dened the norm NL/K (x) of an element x in a eld extension L of K as
the determinant of the multiplication map x . There are two variations over the theme
o
Nimisha Sharma
English B
IB1
Gap Year Proposal
The choice of future career is, perhaps among the most important decision an individual
makes throughout their life. Even though a profession may change with a flow of time, but
taking the first step towards