In algebraic geometry, motives is a theory proposed by Alexander Grothendieck in the 1960s to unify the vast array of similarly behaved cohomology theories ... Introduction · Definition of pure motives · Mixed motives

The Hodge standard conjecture is a positivity statement which implies that the endomor- phism algebra of every motive admits a positive definite involution.

9 авг. 2021 г. · In order to express this kinship of these different cohomological theories, I formulated the notion of “motive” associated to an algebraic ...

18 февр. 2009 г. · This is a major problem, perhaps the major problem, in arithmetic geometry and in algebraic geometry. Conjecture D is known for abelian ...

20 июн. 2010 г. · I am curious as to where I might find a coherent treatment of the theory of motives; one which is below the level of a professional mathematician. What is the status of the theory of motives? - MathOverflow What's the "Yoga of Motives"? - MathOverflow Другие результаты с сайта mathoverflow.net

The quest for a full theory of motives is a potent driving force in complex analysis, algebraic geom- etry, automorphic representation theory, the study of L ...

Motives are rather abstract mathematical entities. Fortunately, we have at our disposal realisation functors that convert a motive into more familiar.

23 февр. 2005 г. · This is an overview and a preview of the theory of mixed motives of level 1 explaining some results, projects, ideas and indicating a bunch of problems.

1 июн. 2017 г. · The idea behind the theory of motives is that all Weil cohomology theories should factor through a “category of motives”.

Considering a (co)homology theory \mathbb{T} on a base category \mathcal{C} as a fragment of a first-order logical theory we here construct an abelian category.