Morel and Voevodsky construct the motivic stable homotopy category, a category through which all cohomology theories factor and where they are representable, by starting with a cat …

I contemplated about what information about a scheme we lose when passing to its motive. I came up with the following examples: The projective bundle of a vector bundle does only …

For all those who are unlikely to have answers to my questions, I provide some Background: In some sense, pure motives are generalisations of smooth projective varieties. Every W …

For the definitions of the equivalence relations on algebraic cycles see http://en.wikipedia.org/wiki/Adequate_equivalence_relation. I want to know how far away from each other th …

In question #7656, Peter Arndt asked why the Gamma function completes the Riemann zeta function in the sense that it makes the functional equation easy to write down. Several of t …

I've heard of this many times, but I don't know anything about it. What I do know is that it is supposed to solve the problem of the fact that the final object in the category of …

Usually the Riemann zeta function $\zeta(s)$ gets multiplied by a "gamma factor" to give a function $\xi(s)$ satisfying a functional equation $\xi(s)=\xi(1-s)$. If I changed this g …

I find the following description of Artin motives in Wikipedia. Since these seem to be quite related to number theory, I am interested to learn more in that context. I request the …

I was wondering when the Kunneth formula holds for motivic cohomology: $$ H^p(X,A(\alpha)) = \bigoplus_{i+j=p;\beta+\gamma = \alpha} H^j(X,A(\beta)) \otimes H^i(X,A(\gamma)) $$ …

SGA 7, tome 1, exp. IX, contains in its introduction and in section 13.4 remarks about ideas and conjectures of Deligne on a “théorie de Néron pour motifs de poids quelconque”. Wou …

Denote $CHM(F)$ to be the category of Chow motives over a field $F$. Let's consider an algebraic exension $E/F$, then there is a natural extension of scalars functor $CHM(F) \to C …

There are some things about geometry that show why a motivic viewpoint is deep and important. A good indication is that Grothendieck and others had to invent some important and new …

Here's a problem that may ultimately require just simple algebraic-geometry skills to be solved, or perhaps it's very deep and will never be solved at all. From the comments, some …

I've read an interesting article, math.NT/0409456 where you're just trying to solve a simple problem: For a given (finite) set of primes S find all solutions to an equation a + …

What are they and what are their intended uses? Does anyone have notes/slides of this talk? I am curious about "log motives" because there seems to exist a "log motivic yoga" amon …