Download PDF by Jean Michel Lemaire: Aigebres Connexes et Homologie des Espaces de Lacets

By Jean Michel Lemaire

ISBN-10: 0387069682

ISBN-13: 9780387069685

Show description

Read Online or Download Aigebres Connexes et Homologie des Espaces de Lacets PDF

Best algebra books

Download e-book for kindle: An Introduction to the Theory of Algebraic Surfaces by Oscar Zariski

Zariski presents an exceptional creation to this subject in algebra, including his personal insights.

Download PDF by Marcus Brazil (auth.), Wieb Bosma, Alf van der Poorten: Computational Algebra and Number Theory

Desktops have stretched the boundaries of what's attainable in arithmetic. extra: they've got given upward push to new fields of mathematical research; the research of latest and conventional algorithms, the construction of latest paradigms for enforcing computational tools, the viewing of outdated strategies from a concrete algorithmic vantage element, to call yet a couple of.

Download e-book for iPad: A First Course in Rings and Ideals by David M. Burton

This quantity is designed to function an creation to the fundamental rules and strategies of ring thought. it's meant to be an expository textbook, instead of a treatise at the topic. The mathematical heritage required for a formal figuring out of the contents isn't really vast. We think that the typical reader has had a few earlier touch with summary algebra yet remains to be particularly green during this recognize.

Extra info for Aigebres Connexes et Homologie des Espaces de Lacets

Sample text

Gal(Q/Q) → Gal(Q/Q) Geometrically, the above setting can be understood in terms of the cyclotomic tower. This has base Spec Z = V1 . The family is Spec Z[ζn ] = Vn where ζn is a primitive n-th root of unity (n ∈ N∗ ). The set Hom (Vm → Vn ), non-trivial for n|m, corresponds to the map Z[ζn ] → Z[ζm ] of rings. The group Aut(Vn ) = GL1 (Z/nZ) is the Galois group Gal(Q(ζn )/Q). The group of symmetries (14) of the tower is then ˆ G = lim GL1 (Z/nZ) = GL1 (Z), ← − n (15) which is isomorphic to the Galois group Gal(Qab /Q) of the maximal abelian extension of Q.

74) In this case, one obtains an algebra homomorphism fg Ug ∈ C0 (X1 ) Γ1 → (fg ◦ π) Uα(g) ∈ C0 (X2 ) Γ2 . (75) When the continuous map π fails to be proper, the above formula only defines a homomorphism to the multiplier algebra C0 (X1 ) Γ1 → M (C0 (X2 ) Γ2 ). In the case of the BC and the GL2 systems, we consider the map α : GL1 (Q) → GL2 (Q) of the form α(r) = r0 01 (76) . We also take π to be the determinant map, (ρ, u) ∈ M2 (Af )×GL2 (R) → π(ρ, u) = (det(ρ), det(u)) ∈ Af ×GL1 (R). (77) We then have the following result extending the classical map of Shimura varieties (70).

For 1 < β ≤ ∞, elements of Eβ are indexed by the classes of invertible ˆ hence by the classical points (16) of the ˆ ∗ = GL1 (Z), Q-lattices ρ ∈ Z noncommutative Shimura variety (26), Eβ ∼ = GL1 (Q)\GL1 (A)/R∗+ ∼ = CQ /DQ ∼ = IQ /Q∗+ , (34) with IQ as in (1). In this range of temperatures, the values of states ϕβ,ρ ∈ Eβ on the elements e(r) ∈ A1,Q is given, for 1 < β < ∞ by polylogarithms evaluated at roots of unity, normalized by the Riemann zeta function, ∞ ϕβ,ρ (e(r)) = 1 n−β ρ(ζrk ). ζ(β) n=1 KMS states and complex multiplication (Part II) 31 ˆ acts by automorphisms of the system.

Download PDF sample

Aigebres Connexes et Homologie des Espaces de Lacets by Jean Michel Lemaire


by Kenneth
4.4

Rated 4.06 of 5 – based on 37 votes