Noncommutative Geometry and Number Theory: Where Arithmetic by Caterina Consani, Matilde Marcolli

By Caterina Consani, Matilde Marcolli

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Famous problems of elementary geometry: the duplication of the cube, the trisection of an angle, the quadrature of the circle: an authorized translation of F. Klein's Vorträge

Extensively considered as a vintage of recent arithmetic, this multiplied model of Felix Klein's celebrated 1894 lectures makes use of modern recommendations to ascertain 3 well-known difficulties of antiquity: doubling the quantity of a dice, trisecting an perspective, and squaring a circle. brand new scholars will locate this quantity of specific curiosity in its solutions to such questions as: below what conditions is a geometrical development attainable?

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R. uk Hilbert modular forms and the Ramanujan conjecture Don Blasius Abstract. This paper completes the proof, at all finite places, of the Ramanujan Conjecture for motivic holomorphic Hilbert modular forms which belong to the discrete series at the infinite places. In addition, the WeightMonodromy Conjecture of Deligne is proven for the Shimura varieties attached to GL(2) and its inner forms, and the conjecture of Langlands, often today called the local-global compatibility , is established at all places for these varieties.

1). Then Fλ is a connected Lie group. We will write Tλ (C) for the standard maximal torus of Fλ . The Weyl group is then W (λ) = Sn1 × · · · × Snp . According to Bourbaki [Bo, Chapter 8], the map Ch, sending each (virtual) representation to its (virtual) character, creates an isomorphism: Ch : R(Fλ ) ∼ = Z[X ∗ (Tλ (C)]W (λ) . Note that a complex linear combination of rational characters of Tλ (C) is precisely a regular function on Tλ (C). For each two-sided cell c of W the Z-submodule Jc of J, spanned by all tw , w ∈ c, is a two-sided ideal of J.

Symp. Pure Math. 3 3 (1979), part 1, 111–155. [CDN] N. Chifan, S. Dascalescu and C. Nastasescu, Wide Morita contexts, relative injectivity and equivalence results, J. Algebra 2 8 4 (2005), 705–736. [C] J. Cuntz, Morita invariance in cyclic homology for nonunital algebras, K-Theory 1 5 (1998), 301 - 305. [CST] J. Cuntz, G. Skandalis, B. Tsygan, Cyclic homology in noncommutative geometry, EMS 1 2 1 , 2004. [EH] D. Eisenbud, J. Harris, The geometry of schemes, Springer Graduate Text 1 9 7 , 2001. [G] M.

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