An arithmetic Riemann-Roch theorem for singular arithmetic surfaces Wayne Aitken. Memoirs of the American Mathematical Society 573.

Aitken, Wayne:

ISBN 10: 0821804073 / ISBN 13: 9780821804070

Published by Providence, American Mathematical Society, 1996

About this Item

Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ancien Exemplaire de bibliothèque avec signature et cachet. BON état, quelques traces d'usure. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. 14 AIT 9780821804070 Sprache: Englisch Gewicht in Gramm: 550.

Seller Inventory # 2501529

Bibliographic Details

• Title: An arithmetic Riemann-Roch theorem for singular arithmetic surfaces Wayne Aitken. Memoirs of the American Mathematical Society 573.
• Publisher: Providence, American Mathematical Society
• Publication Date: 1996
• Language: English
• ISBN 10: 0821804073
• ISBN 13: 9780821804070
• Binding: Softcover
• Weight: 550 grams
• Seller catalogs:
  • SA MATHEMATIK

About this title

Synopsis

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.