Hodge–Witt decomposition of relative crystalline cohomology

Crystalline Cohomology of Superschemes

We introduce a notion of crystalline cohomology for superschemes and show that it is isomorphic to the usual crystalline cohomology of the underlying commutative scheme if 2 is invertible on the base. Wess-Zumino terms play a crucial role in the matching of theoretical predictions in the framework of Quantum Chromodynamics of the decay of the neutral pion π into two photons π −→ γ + γ and the e...

Crystalline Cohomology of Superschemes

We introduce a notion of crystalline cohomology for superschemes and show that it is isomorphic to the usual crystalline cohomology of the underlying commutative scheme if 2 is invertible on the base. Wess-Zumino terms play a crucial role in the matching of theoretical predictions in the framework of Quantum Chromodynamics of the decay of the neutral pion π into two photons π −→ γ + γ and the e...

Crystalline Cohomology and De Rham Cohomology

The goal of this short paper is to give a slightly different perspective on the comparison between crystalline cohomology and de Rham cohomology. Most notably, we reprove Berthelot’s comparison result without using pd-stratifications, linearisations, and pd-differential operators. Crystalline cohomology is a p-adic cohomology theory for varieties in characteristic p created by Berthelot [Ber74]...

Seminar on Crystalline Cohomology

1 Divided Power Algebra—October 31, 2016 1 1.1 Divided Power Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Extension of Divided Power Structure . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Compatible Divided Power structure . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Divided Power Algebra Associated to a Module . . . . . . . . . . . . . . . . . 5 1.5...

Crystalline Cohomology 07gi