Young, Brian. George-Etienne Cartier: Montreal Bourgeois

Limits of Cartier Divisors

Consider a local one-parameter family of Noetherian schemes. More precisely, let f : X → S be a flat map of Noetherian schemes, where S stands for the spectrum of a discrete valuation ring. Let s and η denote the special and generic points of S; putXs := f (s) andXη := f (η). Assume thatXs is of pure dimension and has no embedded components. Let D be an effective Cartier divisor of X. View it a...

Cartier Points on Curves

Throughout this paper Y will denote a complete, nonsingular, and irreducible algebraic curve of genus g > 0 over the algebraically closed field k of characteristic p. Eventually we will assume that g ≥ 2. Denote by W the g-dimensional k-vector space of regular differentials of Y/k, which is just the vector space H(Y,ΩY/k). Also let K(Y ) denote the function field of Y , and let ΩK(Y )/k be the ...

Functorial Cartier Duality

In this paper we obtain the Cartier duality for k-schemes of commutative monoids functorially without providing the vector spaces of functions with a topology (as in [DGr, Exposé VIIB by P. Gabriel, 2.2.1]), generalizing a result for finite commutative algebraic groups by M. Demazure & P. Gabriel ([DG, II, §1, 2.10]). All functors we consider are functors defined over the category of commutativ...

The Birth of Bourgeois Punishment

Michel Etienne: SYLVOPAST

After a brief description of the framework of the model developed to simulate vegetation dynamics, fire propagation and agents' behaviour, the role-playing game rules are presented and related to the different points they are supposed to deal with: climatic hazard, animal grazing, forest management, grazing duty, financial support. The results of several sets of game sessions are analysed accor...