4,877 research outputs found
Comparison Isomorphisms for Smooth Formal Schemes
For a smooth proper scheme or formal scheme over an unramified, complete DVR
of mixed characteristics we prove a comparison isomorphism relating etale
cohomology of the generic fiber with values in a crystalline etale sheaf to the
crystalline cohomology of its special fiber with values in the associated
F-isocrystal
Boolean Coverings of Quantum Observable Structure: A Setting for an Abstract Differential Geometric Mechanism
We develop the idea of employing localization systems of Boolean coverings,
associated with measurement situations, in order to comprehend structures of
Quantum Observables. In this manner, Boolean domain observables constitute
structure sheaves of coordinatization coefficients in the attempt to probe the
Quantum world. Interpretational aspects of the proposed scheme are discussed
with respect to a functorial formulation of information exchange, as well as,
quantum logical considerations. Finally, the sheaf theoretical construction
suggests an opearationally intuitive method to develop differential geometric
concepts in the quantum regime.Comment: 25 pages, Late
Decomposition numbers for perverse sheaves
The purpose of this article is to set foundations for decomposition numbers
of perverse sheaves, to give some methods to calculate them in simple cases,
and to compute them concretely in two situations: for a simple (Kleinian)
surface singularity, and for the closure of the minimal non-trivial orbit in a
simple Lie algebra.
This work has applications to modular representation theory, for Weyl groups
using the nilpotent cone of the corresponding semisimple Lie algebra, and for
reductive algebraic group schemes using the affine Grassmannian of the
Langlands dual group
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