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By J. Ritter

ISBN-10: 0821850938

ISBN-13: 9780821850930

ISBN-10: 2119774374

ISBN-13: 9782119774379

ISBN-10: 2319861432

ISBN-13: 9782319861435

ISBN-10: 3451983699

ISBN-13: 9783451983696

ISBN-10: 4019771952

ISBN-13: 9784019771953

ISBN-10: 5019831611

ISBN-13: 9785019831616

The Langlands software summarizes these components of mathematical learn belonging to the illustration idea of reductive teams and to category box conception. those themes are hooked up by means of the imaginative and prescient that, approximately talking, the irreducible representations of the final linear staff may perhaps function parameters for the outline of all quantity fields. within the neighborhood case, the bottom box is a given $p$-adic box $K$ and the extension concept of $K$ is visible as decided by means of the irreducible representations of absolutely the Galois team $G_K$ of $K$. nice development has been made in setting up correspondence among the supercuspidal representations of $GL(n,K)$ and people irreducible representations of $G_K$ whose levels divide $n$. regardless of those advances, no publication or paper has awarded the diversified equipment used or perhaps gathered identified effects.

This quantity includes the lawsuits of the convention "Representation idea and quantity conception in reference to the neighborhood Langlands Conjecture," held in December 1985 on the college of Augsburg. this system of the convention used to be divided into components: (i) the illustration concept of neighborhood department algebras and native Galois teams, and the Langlands conjecture within the tame case; and (ii) new effects, corresponding to the case $n=p$, the matching theorem, important orders, tame Deligne representations, type of representations of $GL(n)$, and the numerical Langlands conjecture. the gathering of papers during this quantity presents a good account of the present kingdom of the neighborhood Langlands software

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Extra resources for Representation Theory and Number Theory in Connection With the Local Langlands Conjecture: Proceedings of a Conference Held December 8-14, 1985 With

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Therefore Einstein preferred to criticize the foundations of quantum mechanics to save his theory. The main critical argument was presented in the form of a paradox in the foundations of quantum mechanics. This is the so called EPR (1935) paradox [71]. It will be discussed in Chapter 2. Presenting their paradox Einstein, Podolsky and Rosen wanted to save the real model MR of physical reality. However, at the same time their critique of the quantum mechanical formalism was the critique of the same model MR, because the real continuum has been inserted in the foundations of quantum mechanics.

To generalize these examples we consider the space: ° ° Sn,2 °° = {x = (xo, xI, ... ,Xn-1) : Xj = 0, I}. The following ultrametric corresponds to our heuristic ideas about the nearness of social types: P2(X,y) = maxO

1. The ring of rational numbers Q is a subring of each ring ofm-adic integers Qm. In particular, Q is a subfield of each field of p-adic numbers Qp. It is evident that we may construct the rings Qm as completions of Q with respect to pm. It is the standard procedure which is considered in books on number theory [38], [76], [173], [182]. However, we prefer to start with Qm,Jin. Rational numbers are not 'physical numbers' with respect to the m-scale. As we have already said, the quantity L = 1/2 is only an ideal element of Q3.

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Representation Theory and Number Theory in Connection With the Local Langlands Conjecture: Proceedings of a Conference Held December 8-14, 1985 With by J. Ritter


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