nLab rigid cohomology

Rigid cohomology is certain extension of crystalline cohomology to schemes which are not necessarily proper or smooth, introduced in

• Pierre Berthelot, (1986), Géométrie rigide et cohomologie des variétés algébriques de caractéristique p, Mémoires de la Société Mathématique de France. Nouvelle Série (23): 7–32

It is also extending from the affine case the Monsky-Washnitzer cohomology.

The corresponding theory of coefficients is given by overconvergent isocrystals? and more generally arithmetic D-modules.

• Kiran S. Kedlaya, Rigid cohomology and its coefficients, slides, pdf, workshop: p-adic Geometry and Homotopy Theory, Loen, 2009

• Kiran Kedlaya, lecture 20, pdf from a course on algebraic geometry

• wikipedia rigid cohomology

• Denis-Charles Cisinski, Frédéric Déglise, Mixed Weil cohomologies, arxiv/0712.3291

• Bernard le Stum, Rigid cohomology, Cambridge Tracts in Mathematics, 172 (2007)

• David Brown, Rigid cohomology for algebraic stacks, Virginia 2010, slides

Warning: rigid cohomology in contemporary sense should not be confused with the topic of 1977 MacKenzie’s paper Rigid cohomology for topological groupoids (pdf)

See also arithmetic D-modules.