RigidCohomology

DatingbacktoworkofBerthelot,rigidcohomologyappearedasacommongeneralizationofMonsky-Washnitzercohomologyandcrystallinecohomology.Itisap-adicWeilcohomologysuitableforcomputingZetaandL-functionsforalgebraicvarietiesonfinitefields.Moreover,itiseffective,inthesensethatitgivesalgorithmstocomputethenumberofrationalpointsofsuchvarieties.Thisisthefirstbooktogiveacompletetreatmentofthetheory,fromfulldiscussionofallthebasicstodescriptionsoftheverylatestdevelopments.Resultsandproofsareincludedthatarenotavailableelsewhere,localcomputationsareexplained,andmanyworkedexamplesaregiven.Thisaccessibletractwillbeofinteresttoresearchersworkinginarithmeticgeometry,p-adiccohomologytheory,andrelatedcryptographicareas.