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syntomic cohomology

**cohomology** * cocycle, coboundary, coefficient * homology * chain, cycle, boundary * characteristic class * universal characteristic class * secondary characteristic class * differential characteristic class * fiber sequence/long exact sequence in cohomology * fiber ∞-bundle, principal ∞-bundle, associated ∞-bundle, twisted ∞-bundle * ∞-group extension * obstruction ### Special and general types ### * cochain cohomology * ordinary cohomology, singular cohomology * group cohomology, nonabelian group cohomology, Lie group cohomology * Galois cohomology * groupoid cohomology, nonabelian groupoid cohomology * generalized (Eilenberg-Steenrod) cohomology * cobordism cohomology theory * integral cohomology * K-theory * elliptic cohomology, tmf * taf * abelian sheaf cohomology * Deligne cohomology * de Rham cohomology * Dolbeault cohomology * etale cohomology * group of units, Picard group, Brauer group * crystalline cohomology * syntomic cohomology * motivic cohomology * cohomology of operads * Hochschild cohomology, cyclic cohomology * string topology * nonabelian cohomology * principal ∞-bundle * universal principal ∞-bundle, groupal model for universal principal ∞-bundles * principal bundle, Atiyah Lie groupoid * principal 2-bundle/gerbe * covering ∞-bundle/local system * (∞,1)-vector bundle / (∞,n)-vector bundle * quantum anomaly * orientation, Spin structure, Spin^c structure, String structure, Fivebrane structure * cohomology with constant coefficients / with a local system of coefficients * ∞-Lie algebra cohomology * Lie algebra cohomology, nonabelian Lie algebra cohomology, Lie algebra extensions, Gelfand-Fuks cohomology, * bialgebra cohomology ### Special notions * Čech cohomology * hypercohomology ### Variants ### * equivariant cohomology * equivariant homotopy theory * Bredon cohomology * twisted cohomology * twisted bundle * twisted K-theory, twisted spin structure, twisted spin^c structure * twisted differential c-structures * twisted differential string structure, twisted differential fivebrane structure * differential cohomology * differential generalized (Eilenberg-Steenrod) cohomology * differential cobordism cohomology * Deligne cohomology * differential K-theory * differential elliptic cohomology * differential cohomology in a cohesive topos * Chern-Weil theory * ∞-Chern-Weil theory * relative cohomology ### Extra structure * Hodge structure * orientation, in generalized cohomology ### Operations ### * cohomology operations * cup product * connecting homomorphism, Bockstein homomorphism * fiber integration, transgression * cohomology localization ### Theorems * universal coefficient theorem * Künneth theorem * de Rham theorem, Poincare lemma, Stokes theorem * Hodge theory, Hodge theorem nonabelian Hodge theory, noncommutative Hodge theory * Brown representability theorem * hypercovering theorem * Eckmann-Hilton-Fuks duality

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Contents

Idea

Syntomic cohomology is the abelian sheaf cohomology of the syntomic site of a a scheme.

It is closely related to the crystalline cohomology of that scheme.

References

The syntomic site was introduced in

Further developments are in

  • Amnon Besser?, Syntomic regulators and pp-adic integration I: rigid syntomic regulators (pdf)
Created on May 28, 2010 17:10:45 by Urs Schreiber (131.211.36.96)