Some Foundational Questions concerning Differential Algebraic Groups

نویسندگان

  • Anand Pillay
  • ANAND PILLAY
چکیده

In this paper we solve some problems posed by Kolchin about differential algebraic groups. The main result (from which the others follow) is the embeddability of any differential algebraic group in an algebraic group. A crucial intermediate result, and one of independent interest, is a generalisation of Weil’s theorem on recovering an algebraic group from birational data, to pro-algebraic groups.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On Completeness and Linear Dependence for Differential Algebraic Varieties

In this paper we deal with two foundational questions on complete differential algebraic varieties. We establish, by means of the differential algebraic version of Bertini’s theorem and assuming a weaker form of the catenary conjecture, that in order to verify (differential) completeness one can restrict second factors to zero-dimensional differential varieties. Then, we extend Kolchin’s result...

متن کامل

Invariant Differential Equations on Homogeneous Manifolds by Sigurdur Helgason

1. Historical origins of Lie group theory. Nowadays when Lie groups enter in a profound way into so many areas of mathematics, their historical origin is of considerable general interest. The connection between Lie groups and differential equations is not very pronounced in the modern theory of Lie groups, so in this introduction we attempt to describe some of the foundational work of S. Lie, W...

متن کامل

Some Foundational Questions Concerning Language Studies: With a Focus on Categorial Grammars and Model Theoretic Possible Worlds Semantics

There are four major goals for this paper. First, we demonstrate that the logical foundations of standard approaches to language studies involve an incoherence in their presuppositions. Second, we present an alternative approach that resolves this incoherence. Third, we discuss how this error manifests itself in categorial grammars and model theoretic possible worlds semantics. Fourth, we sugge...

متن کامل

ON THE CAPACITY OF EILENBERG-MACLANE AND MOORE SPACES

K. Borsuk in 1979, at the Topological Conference in Moscow, introduced concept of the capacity of a compactum and asked some questions concerning properties of the capacity ofcompacta. In this paper, we give partial positive answers to three of these questions in some cases. In fact, by describing spaces homotopy dominated by Moore and Eilenberg-MacLane spaces, the capacities of a Moore space $...

متن کامل

Some Foundational Issues Concerning Anticipatory Systems

Some foundational conceptual issues concerning anticipatory systems are identified and discussed: 1) The doubly temporal nature of anticipation is noted: anticipations are directed toward one time, and exist at another; 2) Anticipatory systems can be open: they can perturb and be perturbed by states external to the system; 3) Anticipation may be facilitated by a system modeling the relation bet...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1997