In this paper, we show that the maximal divisible subgroup of groups and of an elliptic curve over a function field is uniquely divisible. Further those -groups modulo this uniquely divisible subgroup are explicitly computed. We also calculate the motivic cohomology groups of the minimal regular model of , which is an elliptic surface over a finite field.
On démontre que les plus grands sous-groupes divisibles desgroupes et d’une courbe elliptique sur un corps global de caractéristique positive sont uniquement divisibles et on décrit explicitement les -groupes modulo leurs plus grands sous-groupes divisibles. On calcule également la cohomologie motivique du modèle minimal de qui est une surface elliptique sur un corps fini.
Revised:
Accepted:
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Classification: 11R58, 14F42, 19F27, 11G05
Keywords: K-theory, function field, elliptic curve, motivic cohomology
@article{AIF_2018__68_5_2005_0, author = {Kondo, Satoshi and Yasuda, Seidai}, title = {First and second $K$-groups of an elliptic curve over a global field of positive characteristic}, journal = {Annales de l'Institut Fourier}, pages = {2005--2067}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {68}, number = {5}, year = {2018}, doi = {10.5802/aif.3202}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3202/} }
TY - JOUR TI - First and second $K$-groups of an elliptic curve over a global field of positive characteristic JO - Annales de l'Institut Fourier PY - 2018 DA - 2018/// SP - 2005 EP - 2067 VL - 68 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3202/ UR - https://doi.org/10.5802/aif.3202 DO - 10.5802/aif.3202 LA - en ID - AIF_2018__68_5_2005_0 ER -
%0 Journal Article %T First and second $K$-groups of an elliptic curve over a global field of positive characteristic %J Annales de l'Institut Fourier %D 2018 %P 2005-2067 %V 68 %N 5 %I Association des Annales de l’institut Fourier %U https://doi.org/10.5802/aif.3202 %R 10.5802/aif.3202 %G en %F AIF_2018__68_5_2005_0
Kondo, Satoshi; Yasuda, Seidai. First and second $K$-groups of an elliptic curve over a global field of positive characteristic. Annales de l'Institut Fourier, Volume 68 (2018) no. 5, pp. 2005-2067. doi : 10.5802/aif.3202. https://aif.centre-mersenne.org/articles/10.5802/aif.3202/
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