Vincendon 1 , Y. Langevin 1 , F. Poulet 1 , A. Pommerol 2 , M. J. Wolff 3 , J-P. Bibring 1 , B. Gondet 1 , D. Jouglet 1 , and the OMEGA team, 1 Institut d’Astrophysique Spatiale, CNRS/Université Paris Sud, Orsay, France ([email protected]), 2 Laboratoire de Planétologie de Grenoble, UJF/CNRS, Bât. D de Physique, B.P. 53, 38041 Grenoble Cedex 9, France, 3 Space Science Institute, 1...

These notes outline the “fundamental theorems” of étale cohomology, following [4, Ch. vi], as well as briefly discuss the Weil conjectures.

We develop an approach that allows one to construct semiorthogonal decompositions of derived categories surfaces with cyclic quotient singularities whose components are equivalent local finite-dimensional algebras. first explain how induce a decomposition surface $X$ rational from its resolution. In the case when has singularities, we introduce condition adherence for resolution identify induce...

Building on work of Crew, we give a rigid cohomological analogue of the main result of Deligne’s “Weil II”; this makes it possible to give a purely p-adic proof of the Weil conjectures. Ingredients include a p-adic analogue of Laumon’s application of the geometric Fourier transform in the l-adic setting, as well as recent results on p-adic differential equations, due to André, Christol, Crew, M...

In both of these examples, we have proved that X(Q) = ∅ by showing that X(Qv) = ∅ for some place v. In the first case it was v = ∞, the real place. In the second case we showed that X(Q2) was empty: the argument applies equally well to a supposed solution over Q2. Given a variety X over a number field k and a place v of k, it is a finite procedure to decide whether X(kv) is empty. Moreover, X(k...

Absolute Hodge classes first appear in Deligne’s proof of the Weil conjectures for K3 surfaces in [14] and are explicitly introduced in [16]. The notion of absolute Hodge classes in the singular cohomology of a smooth projective variety stands between that of Hodge classes and classes of algebraic cycles. While it is not known whether absolute Hodge classes are algebraic, their definition is bo...

According to the code of ethics of the National Society of Professional Engineers, engineers must “hold paramount the safety, health, and welfare of the public.” Several kinds of arguments have been employed to show that engineers (and other professionals) have such duties towards the population. Some authors have claimed that these obligations are part of the very essence of professionalism; b...

February 19, 2015 Version 1.8.15 Date 2014/12/17 Title Analysis of habitat selection by animals Author Clement Calenge, contributions from Mathieu Basille, Stephane Dray and Scott Fortmann-Roe Maintainer Clement Calenge Depends R (>= 2.10.0), ade4, tkrplot, shapefiles, sp Suggests spatstat, MASS, CircStats Description A collection of tools for the analysis of hab...