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K-Theory of curves over number fields

✍ Scribed by Andreas Rosenschon; Paul Arne Østvær

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
272 KB
Volume
178
Category
Article
ISSN
0022-4049

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✦ Synopsis

We consider the algebraic K-groups with coe cients of smooth curves over number ÿelds. We give a proof of the Quillen-Lichtenbaum conjecture at the prime 2 and prove explicit corank formulas for the algebraic K-groups with divisible coe cients. At odd primes these formulas assume the Bloch-Kato conjecture, at the prime 2 the formulas hold nonconjecturally.

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✍ V. Suresh 📂 Article 📅 2004 🏛 Elsevier Science 🌐 English ⚖ 290 KB

Let k be a field of characteristic not equal to 2. For nZ1; let H n ðk; Z=2Þ denote the nth Galois Cohomology group. The classical Tate's lemma asserts that if k is a number field then given finitely many elements a 1 ; ?; a n AH 2 ðk; Z=2Þ; there exist a; b 1 ; ?; b n Ak à such that a i ¼ ðaÞ,ðb i