In this monograph, the authors increase a brand new idea of p-adic cohomology for kinds over Laurent sequence fields in confident attribute, in response to Berthelot's idea of inflexible cohomology. Many significant primary homes of those cohomology teams are confirmed, resembling finite dimensionality and cohomological descent, in addition to interpretations by way of Monsky-Washnitzer cohomology and Le Stum's overconvergent website. functions of this new concept to mathematics questions, similar to l-independence and the burden monodromy conjecture, also are discussed.
The building of those cohomology teams, analogous to the Galois representations linked to forms over neighborhood fields in combined attribute, fills a tremendous hole within the research of mathematics cohomology theories over functionality fields. via extending the scope of current equipment, the consequences provided right here additionally function a primary step in the direction of a extra basic thought of p-adic cohomology over non-perfect flooring fields.
Rigid Cohomology over Laurent sequence Fields will supply a useful gizmo for somebody drawn to the mathematics of sorts over neighborhood fields of optimistic attribute. Appendices on vital heritage fabric resembling inflexible cohomology and adic areas make it as self-contained as attainable, and a great place to begin for graduate scholars trying to discover elements of the classical thought of inflexible cohomology and with an eye fixed in the direction of destiny examine within the subject.
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