Arun Ram
Department of Mathematics and Statistics
University of Melbourne
Parkville, VIC 3010 Australia

Department of Mathematics
University of Wisconsin, Madison
Madison, WI 53706 USA

Last updates: 16 November 2009


Let X be a topological space, let x X and let : 𝒯 𝒜 be a functor.

Let 𝒩 X be the neighourhood filter at x .

The stalk of 𝒰 at x is x = lim U 𝒩 x U (direct limit).

Let E = x X x with topology given by setting W open if it satisfies the following constraint. If U 𝒯 and s U then s ~ -1 W is open, where s ~ : U E x s x is given by U x s s x is the natural homomorphism.

The sheafification of is the sheaf ~ given by ~ U = s = s x x U x | if x U then there exists V 𝒯 , and s V such that x V U , and s y y V = s y y V = s : U E | s is continuous and p s ~ = id U where p : E X sends x to x .

We have homomorphisms U ~ U s s x x U .

References [PLACEHOLDER]

[BG] A. Braverman and D. Gaitsgory, Crystals via the affine Grassmanian, Duke Math. J. 107 no. 3, (2001), 561-575; arXiv:math/9909077v2, MR1828302 (2002e:20083)