On a conjecture of Colliot-Th'el`ene concerning quadratic spaces
by
Prof.Ivan Panin(Petersburg Department of Steklov Institute of Mathematics, Russia)
→
Asia/Kolkata
AG-69 (Colaba Campus)
AG-69
Colaba Campus
Description
ABSTRACT:
Let $X$ be an affine smooth complex algebraic variety and let $(V,q)$
be a quadratic space over the ring of regular function on $X$. Let $u$ be an invirtible regular function on $X$. Assume that $q$ represents $u$ over
the rational functions on $X$. We will prove that for any point $x$ in $X$
the space $q$ represents the function $u$ in the local ring $O_{X,x}$ of
the point $x$. This solves in affirmative the conjecture of
Colliot-Th'el`ene mentioned in the title.
