دانلود کتاب Rational Quadratic Forms

The material of the book is largely nineteenth century but the treatment is
structured by two twentieth century insights. The first, which seems to have
come to its full recognition in the work of Hasse and Witt, is that the theory
of forms over fields is logically simpler and more complete than that over
rings. It is therefore appropriate, contrary to what seemed natural earlier,
to study forms with rational coefficients and under rational equivalence
before attacking integral forms and integral equivalence. The second major
insight, due to Hensel and Hasse, is the perspective introduced by the p-adic
view-point. This unveils the majestic simplicity of the logical structure: in
particular it banishes for ever the need for the plethora of multifarious
“characters” and “invariants” which earlier (and some later) authors use to
distinguish forms which are p-adically inequivalent. The p-adic numbers are
as natural as the reals—indeed it can plausibly be argued that they are
logically simpler and that it is only by indoctrination that we feel that the
reals are more familiar. However, as the p-adic numbers are not yet as well-
known as they should be to the broad audience to which this book is addressed,
no knowledge of them has been presupposed.