In algebraic geometry, motives (or sometimes motifs, following French usage) is a theory proposed by Alexander Grothendieck in the 1960's to unify the vast array of similarly behaved cohomology theories such as singular cohomology, de Rham cohomology, etale cohomology, and crystalline cohomology.

2001-02-19 · We reformulate a conjecture of Deligne on 1-motives by using the integral weight filtration of Gillet and Soulé on cohomology, and prove it. This implies the original conjecture up to isogeny. If the degree of cohomology is at most two, we can prove the conjecture for the Hodge realization without isogeny, and even for 1-motives with torsion.

We introduce new motivic invariants of arbitrary varieties over a perfect field. These cohomological invariants take values in the category of one-motives (considered up to isogeny in positive characteristic). The algebraic definition of these invariants presented here proves a conjecture of Deligne. Applications include some cases of conjectures of Serre, Katz and Jannsen on the independence ...

1998-06-01 · We introduce new motivic invariants of arbitrary varieties over a perfect field. These cohomological invariants take values in the category of one-motives (considered up to isogeny in positive characteristic). The algebraic definition of these invariants presented here proves a conjecture of Deligne. Applications include some cases of conjectures of Serre, Katz and Jannsen on the …

This is a question about Deligne's conjecture on special values of L-functions. I have to confess that I've never understood the definition of the determinant which is supposed to give the right special value up to some power of $2\pi i$ and some rational number.

The Deligne conjecture on special values of L-functions is a formulation of the hope for algebraicity of L(n) where L is an L-function and n is an integer in some set depending on L. There is a Deligne conjecture on 1-motives arising in the theory of motives in algebraic geometry .

References. A survey is in. Goncalo Tabuada, A guided tour through the garden of noncommutative motives, in Guillermo Cortinas, Topics in Noncommutative Geometry Clay Mathematics Proceedings Vol 16, 2012 (arxiv1108.3787);; Discussion of Maxim Kontsevich‘s definition of noncommutative motives include. Maxim Kontsevich, Noncommutative motives, talk at the conference on Pierre Deligne’s 61st ...

2012-06-19 · Broadly speaking, Deligne notes that the central subject he is interested in, one of the things he really cares about, can be encapsulated with the code word “motive.” As the standard dictionary definition suggests, a motive tries to get at what lies behind, the motivation, but more specifically and mathematically speaking it is the notion of a common theme linking parallel cohomology theories.

Créer chez quelqu'un les conditions qui le poussent à agir, faire qu'il éprouve de bonnes raisons pour agir : Sa réussite ne peut que le motiver à poursuivre.