Foundations of Pure Mathematics

Every good mathematician is at least half a philosopher,
and every good philosopher is at least half a mathematician. - Frege

Wednesday, September 4, 2024

Elementary Number Theory Algebraic Number Theory (and basis in Galois Theory, Finite Groups and Commutative Algebra) (finite fields, primiti...

Sheaf Theory

Note that a locally constant sheaf is nothing more than a covering space. The definitions of constant and locally constant sheaf are sometim...
Field Theory

Let a field $K$ have characteristic $p > 0$ . Then given $a \in K$ we have that $x - a$ is either irreducible or of the form $(x - b)^{p}$ wi...
Coherent sheaves

The concept of coherent sheaf is of great interest. The definition is subtle but it rests on very basic ideas. Consider a stalk $F_{x}$ of a ...