arXiv subjects
Zacky Choo
Publications and source records attributed to Zacky Choo.
Computing Borel's Regulator
We present an infinite series formula based on the Karoubi-Hamida integral, for the universal Borel class evaluated on H_{2n+1}(GL(\mathbb{C})). For a cyclotomic field F we define a canonical set of elements in K_3(F) and present a novel approach (based on a free differential calculus) to constructing them. Indeed, we are able to explicitly construct their images in H_{3}(GL(\mathbb{C})) under the Hurewicz map. Applying our formula to these images yields a value V_1(F), which coincides with the Borel regulator R_1(F) when our set is a basis of K_3(F) modulo torsion. For F= \mathbb{Q}(e^{2\pi i/3}) a computation of V_1(F) has been made based on our techniques.
$p$-adic Cocycles and their Regulator Maps
We derive a power series formula for the $p$-adic regulator on the higher dimensional algebraic K-groups of number fields. This formula is designed to be well suited to computer calculations and to reduction modulo powers of $p$. In addition we describe a series of regulator questions concerning higher dimensional K-theoretic analogues of conjectures of Gross and Serre.