On the K-theory of curves over finite fields

Kevin R. Coombes

doi:10.1016/0022-4049(88)90079-5

On the K-theory of curves over finite fields

Kevin R. Coombes

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Let X be a smooth projective curve over a finite field. The main result is that the odd-dimensional K-theory of the extension of X to the algebraic closure is the sum of two copies of the K-theory of the field. Two plausible conjectures are advanced which would suffice to compute the K-theory of X itself. These provisional computations are then related to the L-functions of X.

Original language	English (US)
Pages (from-to)	79-87
Number of pages	9
Journal	Journal of Pure and Applied Algebra
Volume	51
Issue number	1-2
DOIs	https://doi.org/10.1016/0022-4049(88)90079-5
State	Published - Mar 1988
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/0022-4049(88)90079-5

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title = "On the K-theory of curves over finite fields",

abstract = "Let X be a smooth projective curve over a finite field. The main result is that the odd-dimensional K-theory of the extension of X to the algebraic closure is the sum of two copies of the K-theory of the field. Two plausible conjectures are advanced which would suffice to compute the K-theory of X itself. These provisional computations are then related to the L-functions of X.",

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N2 - Let X be a smooth projective curve over a finite field. The main result is that the odd-dimensional K-theory of the extension of X to the algebraic closure is the sum of two copies of the K-theory of the field. Two plausible conjectures are advanced which would suffice to compute the K-theory of X itself. These provisional computations are then related to the L-functions of X.

AB - Let X be a smooth projective curve over a finite field. The main result is that the odd-dimensional K-theory of the extension of X to the algebraic closure is the sum of two copies of the K-theory of the field. Two plausible conjectures are advanced which would suffice to compute the K-theory of X itself. These provisional computations are then related to the L-functions of X.

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UR - https://www.scopus.com/pages/publications/38249031372#tab=citedBy

U2 - 10.1016/0022-4049(88)90079-5

DO - 10.1016/0022-4049(88)90079-5

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EP - 87

JO - Journal of Pure and Applied Algebra

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ER -

On the K-theory of curves over finite fields

Abstract

ASJC Scopus subject areas

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