ガロア第一論文と乗数イデアル他関連資料スレ5

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820: １３２人目の素数さん [] 2023/10/28(土) 23:30:56.61 ID:5Ldn12NP

>>819
ありがとう

https://dept.math.lsa.umich.edu/~mattiasj/research.html
Mattias Jonsson Department of Mathematics, University of Michigan,
(I am a professor of mathematics at the University of Michigan)
My research spans across some (but not all!) parts of dynamics, geometry and analysis. In analysis and geometry one usually works with real or complex numbers, but it is also possible to use, for instance, p-adic numbers. Doing so leads to non-Archimedean analysis and geometry, in honor (dishonor?) of Archimedes of Syracuse.

One of my main interests is in how non-Archimedean objects, such as Berkovich spaces, can be used to study problems where the original problem is phrased in terms of complex or rational numbers. Examples include singularities (of psh functions) in complex analysis and the growth of the arithmetic complexity (height) of orbits of certain polynomial, discrete-time, dynamical systems. I am also interested in developing non-Archimedean geometry in a way parallel to complex geometry.

Here is a list of my publications and some lecture notes. For my preprints, see the arXiv. See also google scholar.

https://arxiv.org/abs/1011.3699
Mathematics > Algebraic Geometry
[Submitted on 16 Nov 2010 (v1), last revised 20 Oct 2011 (this version, v3)]
Valuations and asymptotic invariants for sequences of ideals
Mattias Jonsson, Mircea Mustata
We study asymptotic jumping numbers for graded sequences of ideals, and show that every such invariant is computed by a suitable real valuation of the function field. We conjecture that every valuation that computes an asymptotic jumping number is necessarily quasi-monomial. This conjecture holds in dimension two. In general, we reduce it to the case of affine space and to graded sequences of valuation ideals. Along the way, we study the structure of a suitable valuation space.
v3: minor changes, this is the final version, to appear in Ann. Inst. Fourier (Grenoble)

http://rio2016.5ch.net/test/read.cgi/math/1687778456/820

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