TY - BOOK ID - 2816451 TI - Weil conjectures, perverse sheaves, and l'adic Fourier transform AU - Kiehl, Reinhardt AU - Weissauer, Rainer PY - 2001 VL - 42 SN - 3540414576 3642074723 3662045761 PB - Berlin New York Tokyo Springer DB - UniCat KW - Bundeltheorie KW - Cohomology [Sheaf ] KW - Faisceaux [Théorie des ] KW - Homologie KW - Homology theory KW - Sheaf cohomology KW - Sheaf theory KW - Sheaves (Algebraic topology) KW - Sheaves [Theory of ] KW - Théorie des faisceaux KW - Weil conjectures KW - Weil conjectures. KW - Homology theory. KW - Sheaf theory. KW - 512.73 KW - Cohomology, Sheaf KW - Sheaves, Theory of KW - Algebraic topology KW - Cohomology theory KW - Contrahomology theory KW - Conjecture, Weil's KW - Conjectures, Weil KW - Tate conjectures, Weil KW - -Weil-Tate conjectures KW - Weil's conjecture KW - Geometry, Algebraic KW - Cohomology theory of algebraic varieties and schemes KW - 512.73 Cohomology theory of algebraic varieties and schemes KW - Théorie des faisceaux KW - Algebraic geometry. KW - Group theory. KW - K-theory. KW - Algebraic Geometry. KW - Group Theory and Generalizations. KW - K-Theory. KW - Groups, Theory of KW - Substitutions (Mathematics) KW - Algebra KW - Algebraic geometry KW - Geometry UR - https://www.unicat.be/uniCat?func=search&query=sysid:2816451 AB - In this book the authors describe the important generalization of the original Weil conjectures, as given by P. Deligne in his fundamental paper "La conjecture de Weil II". The authors follow the important and beautiful methods of Laumon and Brylinski which lead to a simplification of Deligne's theory. Deligne's work is closely related to the sheaf theoretic theory of perverse sheaves. In this framework Deligne's results on global weights and his notion of purity of complexes obtain a satisfactory and final form. Therefore the authors include the complete theory of middle perverse sheaves. In this part, the l-adic Fourier transform is introduced as a technique providing natural and simple proofs. To round things off, there are three chapters with significant applications of these theories. ER -