A Swan-like theorem

Generating Modules Efficiently: Theorems from Algebraic K-Theory

Several of the fundamental theorems about algebraic K, and Kr are concerned with finding unimodular elements, that is, elements of a projective module which generate a free summand. In this paper we use the notion of a basic element (in the terminology of Swan [22]) to extend these theorems to the context of finitely generated modules. Our techniques allow a simplification and strengthening of ...

A Serre-swan Theorem for Gerbe Modules on Étale Lie Groupoids

Given a torsion bundle gerbe on a compact smooth manifold or, more generally, on a compact étale Lie groupoid M , we show that the corresponding category of gerbe modules is equivalent to the category of finitely generated projective modules over an Azumaya algebra on M . This result can be seen as an equivariant Serre-Swan theorem for twisted vector bundles.

Serre-Swan Theorem for non commutative C∗-algebras

2 00 6 Swan conductors for p - adic differential modules , I : A local construction

We define a numerical invariant, the differential Swan conductor, for certain differential modules on a rigid analytic annulus over a p-adic field. This gives a definition of a conductor for p-adic Galois representations with finite local monodromy over an equal characteristic discretely valued field, which agrees with the usual Swan conductor when the residue field is perfect. We also establis...

Swan conductors for p-adic differential modules, I: A local construction

We define a numerical invariant, the differential Swan conductor, for certain differential modules on a rigid analytic annulus over a p-adic field. This gives a definition of a conductor for p-adic Galois representations with finite local monodromy over an equal characteristic discretely valued field, which agrees with the usual Swan conductor when the residue field is perfect. We also establis...

The Standard Model – the Commutative Case: Spinors, Dirac Operator and De Rham Algebra

The present paper is a short survey on the mathematical basics of Classical Field Theory including the Serre-Swan’ theorem, Clifford algebra bundles and spinor bundles over smooth Riemannian manifolds, Spin-structures, Dirac operators, exterior algebra bundles and Connes’ differential algebras in the commutative case, among other elements. We avoid the introduction of principal bundles and put ...