Download A short course in K-theory by Marc Levine PDF

By Marc Levine

Show description

Read Online or Download A short course in K-theory PDF

Best foreign language dictionaries & thesauruses books

Webster's Korean to English Crossword Puzzles: Level 10

No matter if you don't like crossword puzzles, you'll prove loving those. Designed for mother-tongue or thoroughly fluent audio system of Korean eager to increase their English abilities, the puzzles can also be exciting to English audio system. they're formatted in order that each one puzzle might be solved in 15 to half-hour.

Colloquial Afrikaans: The Complete Course for Beginners

Colloquial Afrikaans presents a step by step path in Afrikaans because it is written and spoken in South Africa and Namibia this present day. Combining a common process with a radical remedy of the language, it equips newcomers with the basic abilities had to speak expectantly and successfully in Afrikaans in a extensive variety of occasions.

Additional resources for A short course in K-theory

Sample text

1) breaking up into short exact sequences jp∗ p/p+1 0 → Kq (MpX ) − → Kq (MX ∂p ) −→ Kq−1 (Mp+1 X ) → 0 for all p and q. 3. Cohomology of K-sheaves. One can go even further with this if one considers the K-sheaves Kp on X, defined as the sheaf associated to the presheaf U → Kp (U ). 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.

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.

Op´erations en K-th´eorie alg´ebrique. Canad. J. Math. 37 (1985), no. 3, 488–550. , Torsion 0-cycles on affine varieties in characteristic p, J. Algebra 120 (1989), no. 2, 428–432. [38] Suslin, A. Algebraic K-theory of fields. Proceedings of the International Congress of Mathematicians, Vol. , 1986), 222–244, Amer. Math. , Providence, RI, 1987. , 1046, Springer, Berlin, 1984. [40] Suslin, A. and Voevodsky, V. M. Annals of Mathematics Studies, 143, Princeton University Press, Princeton, NJ, 2000.

Download PDF sample

Rated 4.16 of 5 – based on 24 votes