By Marc Levine

Show description

Read or Download A short course in K-theory PDF

Best foreign language dictionaries & thesauruses books

Download e-book for iPad: Etymological Dictionary of Scottish-Gaelic by Alexander Macbain, Alexander Macbin

I ordered this e-book early on whilst i started learning Scottish Gaelic, as i wished a source to appear up phrases that weren't on hand in my textbooks. On numerous events i have discovered that the note i used to be searching for was once easily no longer within the dictionary. This dictionary does include attention-grabbing phrases which most probably have cultural hyperlinks to Scotland, for instance rather than having the be aware "cow" they could have fifteen assorted phrases of edition, with meanings like "newborn cow with spots" and different very particular kinds.

Webster's Korean to English Crossword Puzzles: Level 2 by Philip M. Parker PDF

Whether you don't like crossword puzzles, you could prove loving those. Designed for mother-tongue or thoroughly fluent audio system of Korean desirous to enhance their English abilities, the puzzles can also be enjoyable to English audio system. they're formatted in order that each one puzzle will be solved in 15 to half-hour.

New PDF release: The Ultimate French Review and Practice : Mastering French

An outstanding grab of grammar allows the foreign-language learner to construct ability and self belief in communique. here is the "ultimate," painless method for intermediate and complicated freshmen to sweep up at the principles. every one grammatical idea is defined after which illustrated with full of life sentence examples; huge workouts supply perform at employing this data in daily dialog.

Extra resources for A short course in K-theory

Example text

4) 7 (1974), 235–272. , Le th´eor`em de Riemann-Roch, Bull. Soc. Math. France 86 (1958) 97-136. , Surjectivity of cycle maps, in Journ´ ees de Geom´ etrie Alg´ ebrique D’Orsay, Juillet 1992, Ast´erisque 218 (1993) 203226. , Intersection theory. Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 2. Springer-Verlag, Berlin-New York, 1984. , The Bloch-Kato conjecture and a theorem of SuslinVoevodsky, J. Reine Angew. Math. 530 (2001), 55–103. , La th´eorie de classes de Chern, Bull. Soc. Math. France 86 (1958) 137-154.

The stalk Kp,x at x ∈ X is just Kp (OX,x ). 3) 0 → Kq → ⊕x∈X (0) ix∗ (Kq (k(x))) − → d d 1 1 → ⊕x∈X (q) ix∗ (K0 (k(x))). ⊕x∈X (1) ix∗ (Kq−1 (k(x))) − → ... − Here ix : x → X is the inclusion, and we consider Kn (k(x)) as the constant sheaf on the one-point space x. 3) is exact. 3) gives a flasque resolution of the sheaf Kq . 3. Suppose Gersten’s conjecture is true for all the local rings OX,x . 2). In particular, H p (X, Kq ) = 0 if p > q. 3) (after deleting Kq ). 4. Take the case q = 1. Then K1 is just the sheaf of units × OX , and the sheafified Gersten complex is (assume X is irreducible with generic point η) × 1 → OX → iη∗ k(X)× → ⊕x∈X (1) ix∗ Z → 0.

As one consequence, let X be a scheme, and take Z = Xred . Then MX (Z) = MX , and thus Gp (Xred ) → Gp (X) is an isomorphism. 3. , X is a smooth scheme over a field). Then the inclusion PX → MX induces an isomorphism Kp (X) → Gp (X). 46 A SHORT COURSE IN K-THEORY MEXICO CITY MAY, 2002 Indeed, if X is regular and noetherian, each coherent sheaf F on X has a finite resolution by locally free sheaves. 8. 4. Let i : Z → X be the inclusion of a closed subscheme, j : U → X the open complement. Then the sequence BQj ∗ BQi∗ BQ(MZ ) −−−→ BQ(MX ) −−−→ BQ(MU ) is a weak homotopy fiber sequence, so we have a long exact sequence ∂ i j∗ ∗ → Gp (U ) → .

Download PDF sample

A short course in K-theory by Marc Levine

by Brian

Rated 4.49 of 5 – based on 37 votes