HTML and/or PDF files in the folder talklist-cov
For an html and pdf (or ppt) file with the same name, the html is an exposition. Click on any of the [ 2] items below.
An unclickable "Pending" is still in construction. Use [ Comment on ...] buttons to respond to each item, or to the whole page at the bottom.

1. Talk at UCI Irvine in 1995, Weil's Decomposition Theorem, Siegel's Theorem and Néron Divisors, Based on an English translation of Siegel's famous theorem bounding integral points on an affine curve. I use this to motivate Néron's improvement of Weil's distructions – from Weil's Thesis proving the Mordell-Weil generalization of Poincare's conjecture on rational points on an abelian variety. Like Hilbert's irreducibility theorem, the distributions are a general conceptual tool for translating geometry to arithmetic. Since, however, Lang avoided them in his Diophantine Geometry book just about no one older than me knows about them. weildecomp.pdf

2. Oberwolfach 02/08/02 on Field Arithmetic, Talk on Configuration spaces for wildly ramified covers, Arithmetic fundamental groups and noncommutative algebra, PSPUM vol. of the American Math. Society (2002), 223–247. Generalizes to wild ramification one half of Grothendieck's famous deformation approach to the tame fundamental group of an curve in positive characteristic. Does not assume Galois covers, a non-trivial point to go beyond tame ramification. The main construction is the configuration space of covers having a specific type of ramification data – generalization of Herbrand's higher ramification group upper numbering. Main device: explicit computation of all tamely ramified embeddings of a finite extension of a power series in one variable over the algebraic closure of a finite field. oberwolf02-08-02.pdf

For a particular item, use [Comment on ...] buttons after each. Click here to