Witt differentials in the h-topology

Recent important and powerful frameworks for the study of differential forms by Huber-Joerder and Huber-Kebekus-Kelly based on Voevodsky's h-topology have greatly simplified and unified many approaches. This article builds towards the goal of putting Illusie's de Rham-Witt complex in the same framework by exploring the h-sheafification of the rational de Rham-Witt differentials. Assuming resolution of singularities in positive characteristic one recovers a complete cohomological h-descent for all terms of the complex. We also provide unconditional h-descent for the global sections and draw the expected conclusions. The approach is to realize that a certain right Kan extension introduced by Huber-Kebekus-Kelly takes the sheaf of rational de Rham-Witt forms to a qfh-sheaf. As such, we state and prove many results about qfh-sheaves which are of independent interest

Doctor of Philosophy

dissertationThe goal of this work is to construct integral Chern classes and higher cycle classes for a smooth variety over a perfect field of characteristic p > 0 that are compatible with the rigid Chern classes defined by Petrequin. The Chern classes we define have coefficients in the overconvergent de Rham-Witt complex of Davis, Langer and Zink, and the construction is based on the theory of cycle modules discussed by Rost.We prove a comparison theorem in the case of a quasi-projective variety

Full faithfulness for overconvergent F-de Rham-Witt connections

Let X be a smooth variety over a perfect field of characteristic p>0. In this small note we define overconvergent F-de Rham-Witt connections as an analogue for F-crystals over proper schemes. We prove that the forgetful functor from the category of overconvergent F-de Rham-Witt connections to the category of convergent F-de Rham-Witt connections is fully faithful. The argument is an analogue of a discussion by Kedlaya on full faithfulness of overconvergent F-isocrystals.}Comment: 6 pages. Key Words: Witt vectors, overconvergent F-crystals, de Rham-Witt connections, Frobenius, slop

Integral Comparison of Monsky-Washnitzer and overconvergent de Rham-Witt cohomology

The goal of this small note is to extend a result by Christopher Davis and David Zureick-Brown on the comparison between integral Monsky-Washnitzer cohomology and overconvergent de~Rham-Witt cohomology for a smooth variety over a perfect field of positive characteristic p to all cohomological degrees independent of the dimension of the base or the prime number p. Le but de ce travail est de prolonger un r\'esultat de Christopher Davis et David Zureick-Brown concernant la comparaison entre la cohomologie de Monsky-Washnitzer enti\`ere et la cohomologie de de~Rham-Witt surconvergente d'une vari\'et\'e lisse sur un coprs parfait de charact\'eristique positive p \`a tous les degr\'es cohomologiques ind\'epnedent de la dimension de base et du nombre premier p

Differentially expressed transcripts of Tetracapsuloides bryosalmonae (Cnidaria) between carrier and dead‑end hosts involved in key biological processes: novel insights from a coupled approach of FACS and RNA sequencing

Tetracapsuloides bryosalmonae is a malacosporean endoparasite that infects a wide range of salmonids and causes proliferative kidney disease (PKD). Brown trout serves as a carrier host whereas rainbow trout represents a dead-end host. We thus asked if the parasite adapts to the different hosts by changing molecular mechanisms. We used fluorescent activated cell sorting (FACS) to isolate parasites from the kidney of brown trout and rainbow trout following experimental infection with T. bryosalmonae. The sorted parasite cells were then subjected to RNA sequencing. By this approach, we identified 1120 parasite transcripts that were expressed differentially in parasites derived from brown trout and rainbow trout. We found elevated levels of transcripts related to cytoskeleton organisation, cell polarity, peptidyl-serine phosphorylation in parasites sorted from brown trout. In contrast, transcripts related to translation, ribonucleoprotein complex biogenesis and subunit organisation, non-membrane bounded organelle assembly, regulation of protein catabolic process and protein refolding were upregulated in rainbow trout-derived parasites. These findings show distinct molecular adaptations of parasites, which may underlie their distinct outcomes in the two hosts. Moreover, the identification of these differentially expressed transcripts may enable the identification of novel drug targets that may be exploited as treatment against T. bryosalmonae. We here also describe for the first time how FACS based isolation of T. bryosalmonae cells from infected kidney of fish fosters research and allows to define differentially expressed parasite transcripts in carrier and dead-end fish hosts