Superrosy fields and valuations

∗-Valuations and Hermitian Forms on Skew Fields

This paper is a survey of the literature on ways in which the concept of ordering can be extended to the setting of a division ring with involution and the main results for these extensions.

Orderings, Valuations and Hermitian Forms over ∗-fields

Forking and Dividing in Fields with Several Orderings and Valuations

variety). For each i, let φi(x) be a C-dense quantifier-free Li-formula with parameters from K. Then we can find a K-definable rational function f : C → P which is non-constant, and has the property that the divisor f−1(0) is a sum of distinct points in ⋂n i=1 φi(K), with no multipliticities. (In particular, the support of the divisor contains no points from C(K)\C(K) and no points from C \ C.)...

Algebraic Number Theory II: Valuations, Local Fields and Adeles

Thanks to John Doyle, David Krumm and Rankeya Datta for pointing out typos.

VALUATIONS OF p-ADIC REGULATORS OF CYCLIC CUBIC FIELDS

We compute the p-adic regulator of cyclic cubic extensions of Q with discriminant up to 1016 for 3 < p < 100, and observe the distribution of the p-adic valuation of the regulators. We find that for almost all primes the observation matches the model that the entries in the regulator matrix are random elements with respect to the obvious restrictions. Based on this random matrix model a conject...