# On the flat cohomology of binary norm forms

Seminar

Speaker

Dr. Rony Bitan (Université Claude Bernard Lyon I)

Date

04/05/2016 - 11:00 - 10:00Add to Calendar

`2016-05-04 10:00:00``2016-05-04 11:00:00``On the flat cohomology of binary norm forms``In this talk, we will interpret some classical results of Gauss in the language of flat cohomology and extend them. Given a quadratic number field k = Q(\sqrt{d}) with narrow class number h_d^+, let O_d be the orthogonal Z-group of the associated norm form q_k. We will describe the structure of the pointed set H^1_fl(Z, O_d), which classifies quadratic forms isomorphic to q_k in the flat topology, and express its cardinality via h_d^+ and h_{-d}^+. Furthermore, if N_d is the connected component of O_d, we show that any N_d - torsor tensored with itself belongs to the principal genus.``Third floor seminar room``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`Place

Third floor seminar room

Abstract

In this talk, we will interpret some classical results of Gauss in the language of flat cohomology and extend them. Given a quadratic number field k = Q(\sqrt{d}) with narrow class number h_d^+, let O_d be the orthogonal Z-group of the associated norm form q_k. We will describe the structure of the pointed set H^1_fl(Z, O_d), which classifies quadratic forms isomorphic to q_k in the flat topology, and express its cardinality via h_d^+ and h_{-d}^+. Furthermore, if N_d is the connected component of O_d, we show that any N_d - torsor tensored with itself belongs to the principal genus.

Last Updated Date : 25/04/2016