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In mathematics, the Quillen–Lichtenbaum conjecture is a conjecture relating étale cohomology to algebraic K-theory introduced by Quillen, who was inspired by earlier conjectures of Lichtenbaum (1973). Kahn (1997) and Rognes & Weibel (2000) proved the Quillen–Lichtenbaum conjecture at the prime 2 for some number fields. Voevodsky, using some important results of Markus Rost, has proved the Bloch–Kato conjecture, which implies the Quillen–Lichtenbaum conjecture for all primes.
In mathematics, the arithmetic zeta function is a zeta function associated with a scheme of finite type over integers. The arithmetic zeta function generalizes the Riemann zeta function and Dedekind zeta function to higher dimensions. The arithmetic zeta function is one of the most-fundamental objects of number theory.
This is a glossary of algebraic geometry.
In mathematics, more specifically in algebraic geometry, Parshin's conjecture states that for any smooth projective variety X defined over a finite field, the higher algebraic K-groups vanish up to torsion:
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References
- ↑ Kahn, Bruno (2005), "Algebraic K-theory, algebraic cycles and arithmetic geometry", in Friedlander, Eric; Grayson, Daniel (eds.), Handbook of Algebraic K-theory, Berlin, New York: Springer-Verlag, pp. 351–428, CiteSeerX 10.1.1.456.6145 , doi:10.1007/3-540-27855-9_9, ISBN 978-3-540-23019-9 , Theorem 39
- Friedlander, Eric M.; Weibel, Charles W. (1999), An overview of algebraic K-theory, World Sci. Publ., River Edge, NJ, pp. 1–119, MR 1715873 , p. 53