Kernels in the Category of Formal Group Laws
Canadian journal of mathematics, Tome 68 (2016) no. 2, pp. 334-360
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Fontaine described the category of formal groups over the ring of Witt vectors over a finite field of characteristic $p$ with the aid of triples consisting of the module of logarithms, the Dieudonné module, and the morphism from the former to the latter. We propose an explicit construction for the kernels in this category in term of Fontaine's triples. The construction is applied to the formal norm homomorphism in the case of an unramified extension of ${{\mathbb{Q}}_{p}}$ and of a totally ramified extension of degree less or equal than $p$ . A similar consideration applied to a global extension allows us to establish the existence of a strict isomorphism between the formal norm torus and a formal group law coming from $L$ -series.
Mots-clés :
14L05, formal groups, p-divisible groups, Dieudonne modules, norm tori
Demchenko, Oleg; Gurevich, Alexander. Kernels in the Category of Formal Group Laws. Canadian journal of mathematics, Tome 68 (2016) no. 2, pp. 334-360. doi: 10.4153/CJM-2015-024-7
@article{10_4153_CJM_2015_024_7,
author = {Demchenko, Oleg and Gurevich, Alexander},
title = {Kernels in the {Category} of {Formal} {Group} {Laws}},
journal = {Canadian journal of mathematics},
pages = {334--360},
year = {2016},
volume = {68},
number = {2},
doi = {10.4153/CJM-2015-024-7},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-024-7/}
}
TY - JOUR AU - Demchenko, Oleg AU - Gurevich, Alexander TI - Kernels in the Category of Formal Group Laws JO - Canadian journal of mathematics PY - 2016 SP - 334 EP - 360 VL - 68 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-024-7/ DO - 10.4153/CJM-2015-024-7 ID - 10_4153_CJM_2015_024_7 ER -
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