By K. A. Ribet

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**Current Trends in Arithmetical Algebraic Geometry **

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**Extra resources for Current Trends in Arithmetical Algebraic Geometry **

**Example text**

2) A be a discrete subring of a local field K with Let F C K. We assume that (1) A K/A is a compact abelian group. = :It C F = Q C K = IR. C F = lFq(t) = lFq(t- ) C K = IFq«t- (4) A = IFq [C - curve and 00] C F Foo = IFq (C - (0) = IFq (C) C K is the completion of l = Foo F at 00 FC K =C • ». where C is an affine • Of course (3) is a special case of (4),and (4) is the case of interest in this part. given by a norm. exists a neighborhood then Nt of A subgroup 0 in V over H in V with K, the topology is well V is discrete provided there N' n H = O.

Ker(u)(k) u =0 ~a. vu always exists for that u: w(ker(u)(k» = ~ --+-

Norms on vector spaces over a local field ••••••••••••••••••••••• §2. The building for PGL(V) over a local field •••••••••••••••••••• 58 61 § 3. Metric on the building •••••••••••••••••••••••••••••••••••••••••• 63 §4. The mapping from the p-adic symmetric space to the building ••••• 64 §5. Filtration of the I-dimensional p-adic symmetric space •••••••••• 66 © 25 1987 A merican Mathematical Society 26 PIERRE DELIGNE and DALE HUSEMOLLER Chapter 4. Cohomology of the moduli space ••••••••••••••••••••••••••••••• 71 §l.