منابع مشابه
Arakelov Euler Characteristics
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...
متن کاملDiscriminants and Arakelov Euler Characteristics
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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Let E be a modular elliptic curve over [symbol, see text], without complex multiplication; let p be a prime number where E has good ordinary reduction; and let Finfinity be the field obtained by adjoining [symbol, see text] to all p-power division points on E. Write Ginfinity for the Galois group of Finfinity over [symbol, see text]. Assume that the complex L-series of E over [symbol, see text]...
متن کاملEuler characteristics and chromatic polynomials
Given a graph we show how to construct a family of manifolds whose Euler characteristics are the values of the chromatic polynomial of the graph at various integers. The manifolds are simple generalisations of configuration spaces.
متن کاملGaudin functions, and Euler-Poincaré characteristics
Given two positive integers n, r, we define the Gaudin function of level r to be quotient of the numerator of det ( ((xi − yj)(xi − tyj) · · · (xi − tyj)) )
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1968
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1968.26.317