Conjectures in Arithmetic Algebraic Geometry: A Survey - Tapa blanda

Sinopsis

1 The zero-dimensional case: number fields.- 2 The one-dimensional case: elliptic curves.- 3 The general formalism of L-functions, Deligne cohomology and Poincaré duality theories.- 4 Riemann-Roch, K-theory and motivic cohomology.- 5 Regulators, Deligne's conjecture and Beilinson's first conjecture.- 6 Beilinson's second conjecture.- 7 Arithmetic intersections and Beilinson's third conjecture.- 8 Absolute Hodge cohomology, Hodge and Tate conjectures and Abel-Jacobi maps.- 9 Mixed realizations, mixed motives and Hodge and Tate conjectures for singular varieties.- 10 Examples and Results.- 11 The Bloch-Kato conjecture.

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