Abstract Let X / s {X/s} be a proper log smooth scheme of Cartier type over fine whose underlying is the spectrum perfect field κ characteristic p > 0 {p>0} . In this article we prove that cohomology

Let k be a perfect field of positive characteristic and Z an effective Cartier divisor in the projective line over with complement U. In this note, we establish some results about formal deformation theory overconvergent isocrystals on U fixed “local monodromy” along Z. En route, show that Hochschild cochain complex governs deformations module arbitrary associative algebra. We also relate to de...

The purpose of this paper is to give the description of a single algorithm that specializes into several classical transformations derived on words, namely the Cartier-Foata transform, its contextual extension due to Han and the two k-extensions proposed by Clarke and Foata.

For a smooth scheme X of pure dimension d over field k and an effective Cartier divisor D?X whose support is simple normal crossing divisor, we construct cycle class mapcycX|D:CH0(X|D)?HNisd(X,KdM(OX,ID)) from the Chow group zero-cycles with modulus to cohomology relative Milnor K-sheaf.

Vangelis Karkaletsis , Constantine D. Spyropoulos , Dimitris Souflis , Claire Grover , Ben Hachey , Maria Teresa Pazienza , Michele Vindigni , Emmanuel Cartier , José Coch Institute for Informatics and Telecommunications, NCSR “Demokritos” vangelis, costass @iit.demokritos.gr Velti S.A. [email protected] Division of Informatics, University of Edinburgh grover, bhachey @ed.ac.uk D.I.S.P., Unive...

In this article, we propose a geometric analogue of Dirichlet’s unit theorem on arithmetic varieties [18], that is, if X is a normal projective variety over a finite field and D is a pseudo-effective Q-Cartier divisor on X, does it follow that D is Q-effective? We also give affirmative answers on an abelian variety and a projective bundle over a curve.

We present counterexamples to Fujita's conjecture in positive characteristic. More precisely, given any algebraically closed field k of characteristic p>0 and integer m, we show there exists a smooth projective surface S over admitting an ample Cartier divisor A such that the adjoint linear system |KS+mA| is not free base points.

Let (X,∆) be a proper dlt pair and L a nef Cartier divisor such that aL − (KX +∆) is nef and log big on (X,∆) for some a ∈ Z>0. Then |mL| is base point free for every m ≫ 0. 0. Introduction The purpose of this paper is to prove the following theorem. This type of base point freeness was suggested by M. Reid in [Re, 10.4]. Theorem 0.1 (Base point free theorem of Reid-Fukuda type). Assume that (X...