I must preface by confessing complete ignorance in the subject. I've read introductory texts about the theory of motives, but I am certainly no expert.

In http://www.math.ias.edu/files/deligne/GaloisGroups.pdf Deligne talks about (introduces?) the motivic fundamental group. But what is the purpose of this object?

Motives come up in cohomology in order to unify the different Weil cohomologies. But I only know of one way to define the algebraic fundamental group! After all, in cohomology you have a choice of coefficients (in a sheaf), but in the definition of the fundamental group (to my knowledge) there is no equivalent to this. Is the point that just as the algebraic fundamental group classifies etale covers, we can do this for other Grothendieck topologies as well? In what since would the motivic fundamental group unify these?

The above was really one question: i. What theories does the motivic fundamental group unify, and in what sense does it do so?

I will add two more: ii. Is the existence of the motivic fundamental group conjectural?

and

iii. What purpose does the motivic fundamental group serve other than unifying? Deligne makes some references to conjectures that arise as prediction related to the motivic fundamental group. What insight does it provide?

I'm well aware that Deligne's text probably has all the answers to these questions, but I find it to be a hard read, so the more I know coming in the more I will take out of it.

I must preface by confessing complete ignorance in the subject. I've read introductory texts about the theory of motives, but I am certainly no expert.

In http://www.math.ias.edu/files/deligne/GaloisGroups.pdf Deligne talks about (introduces?) the motivic fundamental group. But what is the purpose of this object?

Motives come up in cohomology in order to unify the different Weil cohomologies. But I only know of one way to define the algebraic fundamental group! After all, in cohomology you have a choice of coefficients (in a sheaf), but in the definition of the fundamental group (to my knowledge) there is no equivalent to this. Is the point that just as the algebraic fundamental group classifies etale covers, we can do this for other Grothendieck topologies as well? In what sense would the motivic fundamental group unify these?

The above was really one question: i. What theories does the motivic fundamental group unify, and in what sense does it do so?

I will add two more: ii. Is the existence of the motivic fundamental group conjectural?

and

iii. What purpose does the motivic fundamental group serve other than unifying? Deligne makes some references to conjectures that arise as prediction related to the motivic fundamental group. What insight does it provide?

I'm well aware that Deligne's text probably has all the answers to these questions, but I find it to be a hard read, so the more I know coming in the more I will take out of it.

I must preface by confessing complete ignorance in the subject. I've read introductory texts about the theory of motives, but I am certainly no expert.

In http://www.math.ias.edu/files/deligne/GaloisGroups.pdf Deligne talks about (introduces?) the motivic fundamental group. But what is the purpose of this object?

Motives come up in cohomology in order to unify the different Weil cohomologies. But I only know of one way to define the algebraic fundamental group! After all, in cohomology you have a choice of coefficients (in a sheaf), but in the definition of the fundamental group (to my knowledge) there is no equivalent to this. Is the point that just as the algebraic fundamental group classifies etale covers, we can do this for other Grothendieck topologies as well? In what since would the motivic fundamental group unify these?

The above was really one question: i. What theories does the motivic fundamental group unify, and in what sense does it do so?

I will add two more: ii. Is the existence of the motivic fundamental group conjectural?

and

iii. What purpose does the motivic fundamental group serve other than unifying? Deligne makes some references to conjectures that arise as prediction related to the motivic fundamental group. What insight does it provide?

I'm well aware that Deligne's text probably has all the answers to these questions, but I find it to be hard read, so the more I know coming in the more I will take out of it.

I must preface by confessing complete ignorance in the subject. I've read introductory texts about the theory of motives, but I am certainly no expert.

In http://www.math.ias.edu/files/deligne/GaloisGroups.pdf Deligne talks about (introduces?) the motivic fundamental group. But what is the purpose of this object?

Motives come up in cohomology in order to unify the different Weil cohomologies. But I only know of one way to define the algebraic fundamental group! After all, in cohomology you have a choice of coefficients (in a sheaf), but in the definition of the fundamental group (to my knowledge) there is no equivalent to this. Is the point that just as the algebraic fundamental group classifies etale covers, we can do this for other Grothendieck topologies as well? In what since would the motivic fundamental group unify these?

The above was really one question: i. What theories does the motivic fundamental group unify, and in what sense does it do so?

I will add two more: ii. Is the existence of the motivic fundamental group conjectural?

and

iii. What purpose does the motivic fundamental group serve other than unifying? Deligne makes some references to conjectures that arise as prediction related to the motivic fundamental group. What insight does it provide?

I'm well aware that Deligne's text probably has all the answers to these questions, but I find it to be a hard read, so the more I know coming in the more I will take out of it.