A new p-adic cohomology in characteristic p

Inhaltsangabe / Literatur / empfohlene Vorkenntnisse The etale cohomology of Artin and Grothendieck works very well for coefficients which are invertible on the considered scheme. For a prime and p-coefficients in characteristic p the crystalline cohomology gives a good theory, except for the case of integral and torsion coefficients. The problem is that the Frobenius action cannot be inverted. The course will present a refined cohomology, the so-called F-gauge-cohomology, which remedies these problems. It improves several other p-adic cohomology theories as well. Literature: Manuscript `Frobenius gauges and a new theory of p-torsion sheaves in characteristic p’ This course is a good continuation of the course `Etale Kohomologie’ from SS 2013 or `Algebraic Geometry III’ from WS 2012/13

Course description The etale cohomology of Artin and Grothendieck works very well for coefficients which are invertible on the considered scheme. For a prime and p-coefficients in characteristic p the crystalline cohomology gives a good theory, except for the case of integral and torsion coefficients. The problem is that the Frobenius action cannot be inverted. The course will present a refined cohomology, the so-called F-gauge-cohomology, which remedies these problems. It improves several other p-adic cohomology theories as well. Literature: Manuscript `Frobenius gauges and a new theory of p-torsion sheaves in characteristic p’ This course is a good continuation of the course `Etale Kohomologie’ from SS 2013 or `Algebraic Geometry III’ from WS 2012/13