Noncommutative Geometry, Quantum Fields and Motives

1-dimensional 2-dimensional Q-lattices abelian adele class space affine group scheme automorphisms bundle C*-algebra Chapter coefficients cohomology commensurability commutative compact condition consider construction corresponding counterterms cyclic cyclic cohomology cyclic modules defined Definition denote dimension Dirac operator dual elements endomorphisms endomotives equation equisingular equivalence explicit fact factor fermions field theory finite following result Fourier transform functor Galois group gauge given gives group scheme groupoid Haar measure Higgs Hilbert space homomorphism Hopf algebra inner fluctuations integral isomorphism L-functions Lagrangian Lemma linear matrix modular module morphism motives multiplication neutrino noncommutative geometry noncommutative space normalization notation obtained pair parameters Proof Proposition quantum statistical mechanical quark quotient relation renormalization representation restriction Riemann satisfies scaling Shimura variety shows spectral action spectral triple Standard Model subalgebra subgroup subspace symmetries Tannakian Tannakian category tensor Theorem trace formula values vector von Neumann algebra zero zeta function