On the flat cohomology of binary norm forms

Rony A. Bitan; Michael M. Schein

doi:10.5802/jtnb.1093

On the flat cohomology of binary norm forms

Rony A. Bitan, Michael M. Schein

Department of Mathematics

Afeka Tel Aviv Academic College of Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

Let O be√an order of index m in the maximal order of a quadratic number field k = Q( d). Let O_d,m be the orthogonal Z-group of the associated norm form q_d,m. We describe the structure of the pointed set H_fl¹(Z, O_d,m), which classifies quadratic forms isomorphic (properly or improperly) to q_d,m in the flat topology. Gauss classified quadratic forms of fundamental discriminant and showed that the composition of any binary Z-form of discriminant ∆_k with itself belongs to the principal genus. Using cohomological language, we extend these results to forms of certain non-fundamental discriminants.

Original language	English
Pages (from-to)	527-553
Number of pages	27
Journal	Journal de Theorie des Nombres de Bordeaux
Volume	31
Issue number	3
DOIs	https://doi.org/10.5802/jtnb.1093
State	Published - 2019

Bibliographical note

Publisher Copyright:
© Société Arithmétique de Bordeaux, 2019, tous droits réservés.

Funding

Manuscrit reçu le 3 novembre 2016, révisé le 24 juin 2019, accepté le 28 septembre 2019. 2010 Mathematics Subject Classification. 11E41, 11E72, 11E12. Mots-clefs. flat cohomology, quadratic forms, quadratic orders. This work was supported by grant 1246/2014 from the Germany-Israel Foundation. The first author was also supported by a Chateaubriand Fellowship of the Embassy of France in Israel, 2016.

Funders	Funder number
Germany-Israel Foundation

Keywords

Fat cohomology
Quadratic forms
Quadratic orders

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10.5802/jtnb.1093

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On the flat cohomology of binary norm forms

Abstract

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Keywords

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