Nonstandard étale cohomology

Notes on Étale Cohomology

à 4.0 Short Comment on Sheaves, Bundles, and Representable Functors. The notion of a sheaf over a topological space X generalize that of a bundle over X . We're more-or-less aware of this. I want to spend some time looking the specifics of this generalization. I'll focus on schemes. Fix a ring A and let 1 :=A 1 be the affine line. The first thing I want to point out is that the global section...

Nonstandard Étale Cohomology

A lot of good properties of étale cohomology only hold for torsion coefficients. We use “enlargement of categories” as developed in [BS] to define a cohomology theory that inherits the important properties of étale cohomology while allowing greater flexibility with the coefficients. In particular, choosing coefficients Z/P Z (for P an infinite prime and Z the enlargement of Z) gives a Weil coho...

Étale Lattices over Quadratic Integers

We construct lattices with quadratic structure over the integers in quadratic number fields having the property that the rank of the quadratic structure is constant and equal to the rank of the lattice in all reductions modulo maximal ideals. We characterize the case in which such lattices are free. The construction gives a representative of the genus of such lattices as an orthogonal sum of “s...

Effective Étale - Descent Morphisms in M - Ordered Sets Pier Giorgio

Following the results obtained in Preord and in Cat, we characterize the effective étale-descent morphisms inM -Ord, the category ofM -ordered sets for a given monoid M . Furthermore we show that in M -Ord every effective descent morphism is effective for étale-descent (while the converse is false), and we generalize it to a more general context of relational algebras.

FOUNDATIONS OF NONSTANDARD ANALYSIS A Gentle Introduction to Nonstandard Extensions