Here, we will get halfway into constructing $M_{cyc}$. We will try to understand the topology of the prime ideal spectrum $\mathbf{Spec}(\mathbb{C}[\overline{\mathbb{Q}}^{\times}])$ of the complex group algebra of the multiplicative group $\overline{\mathbb{Q}}^{\times}$ of all non-zero algebraic numbers. Take an Abelian locally compact group $A$ (for example, an Abelian group equipped with the discrete topology), then its.

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Academics / Mathematics : The n-Category Caf

Two obscure-seeming kinds of generalized operad help make categorical sense out of two constructions in classical algebraic topology.

Academics / Mathematics : Ars Mathematica

J. P. May’s book, A Concise Course in Algebraic Topology, is available for download on his homepage. The book provides an overview of classical algebraic topology: homology and homotopy groups, K-theory, and cobordism.

Academics / Mathematics : Secret Blogging Seminar

The first definition in “Grothendieck-style” algebraic geometry is the affine scheme for any ring. This is a topological space whose set of points in the set of prime ideals in. Then one defines a scheme to be a locally ringed space...

Academics / Mathematics : Neverendingbooks

TweetOne of the coolest (pure math) facts in Conway’s book ONAG is the explicit construction of the algebraic closure $\overline{\mathbb{F}_2}$ of the field with two elements as the set of all ordinal numbers smaller than $(\omega^{...

Academics / Mathematics : Neverendingbooks

Absolute geometry is the attempt to develop algebraic geometry over the elusive field with one element $\mathbb{F}_1$. The idea being that the set of all prime numbers is just too large for $\mathbf{Spec}(\mathbb{Z})$ to be a termin...

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