Contents

Preface ix

List of Participants xi

H1(X,

ν) of conics and Witt kernels in characteristic 2

R. Aravire and B. Jacob 1

Pythagoras numbers and quadratic ﬁeld extensions

K.J. Becher and D.B. Leep 21

On perfection relations in lattices

A.-M.

Berg´

e and J. Martinet 29

Linear independence of local densities of quadratic forms and its application

to the theory of Siegel modular forms

S. Bocherer,

¨

Y. Hironaka, and F. Sato 51

Representation of reduced special groups in algebras of continous functions

M. Dickmann and F. Miraglia 83

Solubility of Fermat equations

T.D. Browning and R. Dietmann 99

Multiplicative properties of integral binary quadratic forms

A.G. Earnest and R.W. Fitzgerald 107

Eﬀective structure theorems for symplectic spaces via height

L. Fukshansky 117

Orthogonal involutions on algebras of degree 16 and the Killing form of E8

(with an appendix by Kirill Zainoulline)

S. Garibaldi 131

The ﬁrst Zariski cohomology group of the Witt sheaf over a split simply

connected simple algebraic group

S. Gille 163

On families of testing formulae for a pp formula

P. G ladki and M. Marshall 181

Siegel modular forms of small weight and the Witt operator

T. Ibukiyama and S. Wakatsuki 189

On isotropy of quadratic pairs

N.A. Karpenko 211

vii