Frobenius–Ehresmann structures and Cartan geometries in positive characteristic

The aim of the present paper is to lay foundation for a theory Ehresmann structures in positive characteristic, generalizing Frobenius-projective and Frobenius-affine defined previous work. This deals with atlases étale coordinate charts on varieties modeled homogeneous spaces algebraic groups, which we call Frobenius–Ehresmann structures. These are compared Cartan geometries as well higher-dimensional generalizations dormant indigenous bundles. In particular, investigate conditions under these geometric equivalent each other. Also, consider classification problem curves. latter half discusses deformation bundles setting. tangent obstruction various functors computed terms hypercohomology groups certain complexes. As consequence, formulate prove Ehresmann–Weil–Thurston principle fact asserts that deformations variety equipped structure completely determined by their monodromy crystals.