As an introduction to Shimura varieties, and, in particular, to Deligne’s Bourbaki and Corvallis talks (Deligne 1971, 1979), I explain the main ideas and results of the general theory of Shimura varieties in the context of Shimura curves. These notes had their origin in a two-hour lecture I gave on September 10, 2002. They are available at www.jmilne.org/math/. Please send corrections and comments to me at

An approach for intermediate-level simulation of carbon allocation in functional-structural plant models

We prove the existence of integral canonical models of Shimura varieties of preabelian type with respect to primes of characteristic at least 5.

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• Aggregate dividends Dt are i.i.d. dDt

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We develop a framework of characteristics, essential and recommended, that a data model should have to be suitable as canonical model for federated databases. This framework is based on the two factors of the representation ability of a model: expressiveness and semantic relativism. Several data

We give refined statements and modern proofs of Rosenlicht’s results about the canonical model C′ of an arbitrary complete integral curve C. Notably, we prove that C and C′ are birationally equivalent if and only if C is nonhyperelliptic, and that, if C is nonhyperelliptic, then C′ is equal

Canonical models are very useful for determining simple representation formalism for qualitative relations. Allen's interval relations, e.g., can thereby be represented using the start and the end point of the intervals. Such a simple representation was not possible for regions of higher

Abstract. We show that the GIT quotients of suitable loci in the Hilbert and Chow schemes of 4-canonically embedded curves of genus g ≥ 3 are the moduli space M ps g of pseudostable curves constructed by Schubert in [9] using Chow varieties and 3-canonical models. The only new ingredient needed