Pythagoras numbers of function fields of hyperelliptic curves with good reduction

DOI10.1007/s00229-005-0618-6zbMath1120.14016OpenAlexW2110553833MaRDI QIDQ818804

Sergey V. Tikhonov, Jan Van Geel, Vyacheslav I. Yanchevskiĭ

Publication date: 21 March 2006

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00229-005-0618-6

zbMATH Keywords

sums of squaresPythagoras numberBrauer groupformal power series field

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Galois cohomology (12G05) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Algebraic functions and function fields in algebraic geometry (14H05)

Related Items (7)

A ruled residue theorem for function fields of elliptic curves ⋮ Nonsplit conics in the reduction of an arithmetic curve ⋮ Bounding the Pythagoras number of a field by \(2^n +1\) ⋮ Note on Conic Bundles over Henselian Discrete Valued Fields with Real Closed Residue Field ⋮ Sums of squares in function fields of hyperelliptic curves ⋮ A cubic ring of integers with the smallest Pythagoras number ⋮ Pythagoras numbers of orders in biquadratic fields

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