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Integral differentials of elliptic function fields

Integral differentials of elliptic function fields Abh. Math. Sem. Univ. Hamburg 74 (2004), 243-252 By E. KUNZ and R. WALDI 1 Introduction Let K be an arithmetic function field of transcendence degree r over a number field k, that is the field of rational functions of an irreducible r-dimensional algebraic variety defined over k. Let A be the ring of integers of k. We denote by V the set of all discrete valuation rings R with quotient field Q(R) = K which are essentially of finite type over A. Moreover we set Vs := {R e V I R is smooth over A}. If R e V contains k, then R is certainly smooth over A. If mR N A =: p is a maximal ideal of A smoothness of R over A simply means that mR = pR. KAHLER [3] has introduced the module of integral differential forms of K with respect to the different. It is the graded A-module D( K A):= A ~(R/A)-I[R'dR] ReV where [R, dR] is the canonical image of f2R/a in f2K/k and O(R/A) the r-th K~ihler D K different of R/A. With this notation the module D(if) studied in [4] is (TIZ). By the product formula for the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Springer Journals

Integral differentials of elliptic function fields

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References (5)

Publisher
Springer Journals
Copyright
Copyright © 2004 by Mathematische Seminar
Subject
Mathematics; Algebra; Differential Geometry; Combinatorics; Number Theory; Topology; Geometry
ISSN
0025-5858
eISSN
1865-8784
DOI
10.1007/BF02941539
Publisher site
See Article on Publisher Site

Abstract

Abh. Math. Sem. Univ. Hamburg 74 (2004), 243-252 By E. KUNZ and R. WALDI 1 Introduction Let K be an arithmetic function field of transcendence degree r over a number field k, that is the field of rational functions of an irreducible r-dimensional algebraic variety defined over k. Let A be the ring of integers of k. We denote by V the set of all discrete valuation rings R with quotient field Q(R) = K which are essentially of finite type over A. Moreover we set Vs := {R e V I R is smooth over A}. If R e V contains k, then R is certainly smooth over A. If mR N A =: p is a maximal ideal of A smoothness of R over A simply means that mR = pR. KAHLER [3] has introduced the module of integral differential forms of K with respect to the different. It is the graded A-module D( K A):= A ~(R/A)-I[R'dR] ReV where [R, dR] is the canonical image of f2R/a in f2K/k and O(R/A) the r-th K~ihler D K different of R/A. With this notation the module D(if) studied in [4] is (TIZ). By the product formula for the

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Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals

Published: Aug 28, 2008

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