$\ep$-constants and Arakelov Euler characteristics
نویسندگان
چکیده
منابع مشابه
ε-constants and equivariant Arakelov Euler characteristics
Let R[G] be the group ring of a finite group G over a ring R. In this article, we study Euler characteristics of bounded metrised complexes of finitely generated Z[G]-modules, with applications to Arakelov theory and the determination of ǫ-constants. A metric on a bounded complex K• of finitely generated Z[G]-modules is specified by giving for each irreducible character φ of G a metric on the d...
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The study of discriminants has been a central part of algebraic number theory (c.f. [30]), and has recently led to striking results in arithmetic geometry (e.g. [6], [33], [2]). In this article we summarize two different generalizations ([16], [11]) of discriminants to arithmetic schemes having a tame action by a finite group. We also discuss the results proved in [11, 15, 16] concerning the co...
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Fröhlich suggested considering invariants of ON together with the trace pairing (x, y) → TrN/Q(xy). This leads to local and global Hermitian discriminants of (ON, Tr) in “Hermitian classgroups.” Cassou-Noguès and Taylor showed these discriminants were enough to determine both local and global symplectic root numbers. This approach will be generalized to projective schemes over Z in lecture 3. O...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2000
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2000.v7.n4.a9