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...

This is an expository paper on zeta functions of abelian varieties over finite fields. We would like to go through how zeta function is defined, and discuss the Weil conjectures. The main purpose of this paper is to fill in more details to the proofs provided in Milne. Subject to length constrain, we will not include a detailed proof for Riemann hypothesis in this paper. We will mainly be follo...

First of all, we find some further properties of the characterization of fiber product preserving bundle functors on the category of all fibered manifolds in terms of an infinite sequence A of Weil algebras and a double sequenceH of their homomorphisms from [5]. Then we introduce the concept of Weilian prolongation WA HS of a smooth category S over N and of its action D. We deduce that the func...