Class Field Theory - Purdue Math

... Let K be a number field, A = OK , and p a prime ideal of K. The localization Ap is a discrete valuation ring whose normalized valuation we denote by ordp or νp . To describe this valuation more explicitly, let π be a generator of the unique maximal ideal of Ap . Then every x ∈ K ∗ can be uniquely wr ...

... Let K be a number field, A = OK , and p a prime ideal of K. The localization Ap is a discrete valuation ring whose normalized valuation we denote by ordp or νp . To describe this valuation more explicitly, let π be a generator of the unique maximal ideal of Ap . Then every x ∈ K ∗ can be uniquely wr ...

pdf-file. - Fakultät für Mathematik

... after all, any group algebra has, for trivial reasons, a basis with the multiplicative property (1), but usually will not have a multiplicative Cartan basis. The main result of [B-S] asserts that any representation-finite, as well as any minimal representation-infinite algebra, has a multiplicative ...

... after all, any group algebra has, for trivial reasons, a basis with the multiplicative property (1), but usually will not have a multiplicative Cartan basis. The main result of [B-S] asserts that any representation-finite, as well as any minimal representation-infinite algebra, has a multiplicative ...

Automorphisms of 2--dimensional right

... about the automorphism groups of general right-angled Artin groups. In this paper we begin a systematic study of automorphism groups of right-angled Artin groups. We restrict our attention to the case that the defining graph is connected and triangle-free or, equivalently, A is freely indecomposa ...

... about the automorphism groups of general right-angled Artin groups. In this paper we begin a systematic study of automorphism groups of right-angled Artin groups. We restrict our attention to the case that the defining graph is connected and triangle-free or, equivalently, A is freely indecomposa ...

Introduction to derived algebraic geometry

... However, this construction depends on the choice of “generators and relations” for X. We’d like something which doesn’t depend on such a presentation. This is what derived schemes are all about: X should carry some extra structure in a way that the obstruction space and the obstructions themselves a ...

... However, this construction depends on the choice of “generators and relations” for X. We’d like something which doesn’t depend on such a presentation. This is what derived schemes are all about: X should carry some extra structure in a way that the obstruction space and the obstructions themselves a ...

ppt slides

... Artin’s representation is obtained from considering braids as mapping classes The disk is made of rubber Punctures are holes The braid is made of wire The disk is being pushed down along the braid ...

... Artin’s representation is obtained from considering braids as mapping classes The disk is made of rubber Punctures are holes The braid is made of wire The disk is being pushed down along the braid ...

Emil Artin (German: [ˈaɐ̯tiːn]; March 3, 1898 – December 20, 1962) was an Austrian mathematician. Artin was one of the leading mathematicians of the twentieth century. He is best known for his work on algebraic number theory, contributing largely to class field theory and a new construction of L-functions. He also contributed to the pure theories of rings, groups and fields.