200 research outputs found
Another Combinatorial Determinant
We present a variation and generalization of a determinant evaluation of Wilf
(math.CO/9809120). His result concerns a matrix whose entries are the
coefficients of powers of a given power series; we replace the powers by
repeated compositions and obtain similar results.Comment: 3 pages, AMSLaTeX source (replaced 18 May 1998: corrected some typos,
added a reference provided by Herb Wilf
Relative p-adic Hodge theory and Rapoport-Zink period domains
As an example of relative p-adic Hodge theory, we sketch the construction of
the universal admissible filtration of an isocrystal (\phi$-module) over the
completion of the maximal unramified extension of Q_p, together with the
associated universal crystalline local system.Comment: 20 page
Automorphisms of perfect power series rings
Let R be a perfect ring of characteristic p. We show that the group of
continuous R-linear automorphisms of the perfect power series ring over R is
generated by the automorphisms of the ordinary power series ring together with
Frobenius; this answers a question of Jared Weinstein.Comment: 4 pages; v3: final submitted versio
On commutative nonarchimedean Banach fields
We study the problem of whether a commutative nonarchimedean Banach ring
which is algebraically a field can be topologized by a multiplicative norm.
This can fail in general, but it holds for uniform Banach rings under some mild
extra conditions. Notably, any perfectoid ring whose underlying ring is a field
is a perfectoid field.Comment: 14 pages; v7: includes corrections to published versio
Convergence polygons for connections on nonarchimedean curves
This is a survey article on ordinary differential equations over
nonarchimedean fields based on the author's lecture at the 2015 Simons
Symposium on nonarchimedean and tropical geometry. Topics include: the
convergence polygon associated to a differential equation (or a connection on a
curve); links to the formal classification of differential equations
(Turrittin-Levelt); index formulas for de Rham cohomology of connections;
ramification of finite morphisms; relations with the Oort lifting problem on
automorphisms of curves. The appendices include some new technical results and
an extensive thematic bibliography.Comment: v2: final refereed version; one appendix withdrawn, other minor
correction
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