An Arithmetic Riemann-Roch Theorem for Singular Arithmetic Surfaces (Memoirs of the American Mathematical Society)

by: Wayne Aitken

: An Arithmetic Riemann-Roch Theorem for Singular Arithmetic Surfaces (Memoirs of the American Mathematical Society)

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Binding: Paperback
EAN: 9780821804070
ISBN: 0821804073
Label: Amer Mathematical Society
Manufacturer: Amer Mathematical Society
Number Of Pages: 174
Publication Date: 1996-02
Publisher: Amer Mathematical Society
Sales Rank: 7486411
Studio: Amer Mathematical Society

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Product Description:
The first half of this work gives a treatment of Deligne's functorial intersection theory tailored to the needs of this paper. This treatment is intended to satisfy three requirements: 1) that it be general enough to handle families of singular curves, 2) that it be reasonably self-contained, and 3) that the constructions given be readily adaptable to the process of adding norms and metrics such as is done in the second half of the paper.

The second half of the work is devoted to developing a class of intersection functions for singular curves that behaves analogously to the canonical Green's functions introduced by Arakelov for smooth curves. These functions are called intersection functions since they give a measure of intersection over the infinite places of a number field. The intersection over finite places can be defined in terms of the standard apparatus of algebraic geometry.

Finally, the author defines an intersection theory for arithmetic surfaces that includes a large class of singular arithmetic surfaces. This culminates in a proof of the arithmetic Riemann-Roch theorem.

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