It is by now a well-known paradigm that public-key cryptosystems can be built using finite Abelian groups and that algebraic geometry provides a supply of such groups through Abelian varieties over finite fields. Of special interest are the Abelian varieties that are Jacobians of algebraic curves. All of the articles in this volume are centered on the theme of point counting and explicit arithmetic on the Jacobians of curves over finite fields. The topics covered include Schoof's $ell$-adic point counting algorithm, the $p$-adic algorithms of Kedlaya and Denef-Vercauteren, explicit arithmetic...
It is by now a well-known paradigm that public-key cryptosystems can be built using finite Abelian groups and that algebraic geometry provides a suppl...
This monograph brings together a collection of results on the non-vanishing of- functions.Thepresentation, thoughbasedlargelyontheoriginalpapers, issuitable forindependentstudy.Anumberofexerciseshavealsobeenprovidedtoaidinthis endeavour. The exercises are of varying di?culty and those which require more e?ort have been marked with an asterisk. The authors would like to thank the Institut d'Estudis Catalans for their encouragementof thiswork throughtheFerranSunyeriBalaguerPrize.Wewould also like to thank the Institute for Advanced Study, Princeton for the excellent conditions which made this...
This monograph brings together a collection of results on the non-vanishing of- functions.Thepresentation, thoughbasedlargelyontheoriginalpapers, issu...