In this monograph, the authors advance a brand new conception of p-adic cohomology for forms over Laurent sequence fields in confident attribute, in response to Berthelot's thought of inflexible cohomology. Many significant basic houses of those cohomology teams are confirmed, reminiscent of finite dimensionality and cohomological descent, in addition to interpretations when it comes to Monsky-Washnitzer cohomology and Le Stum's overconvergent web site. purposes of this new thought to mathematics questions, reminiscent of l-independence and the load monodromy conjecture, also are discussed.
The development of those cohomology teams, analogous to the Galois representations linked to kinds over neighborhood fields in combined attribute, fills a big hole within the research of mathematics cohomology theories over functionality fields. through extending the scope of present tools, the consequences offered the following additionally function a primary step in the direction of a extra normal concept of p-adic cohomology over non-perfect floor fields.
Rigid Cohomology over Laurent sequence Fields will supply a great tool for an individual drawn to the mathematics of sorts over neighborhood fields of optimistic attribute. Appendices on vital history fabric akin to 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 a watch in the direction of destiny learn within the subject.
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