# Tag Info

Accepted

### Tannakian Formalism for the Quaternions and Dihedral Group

Let $V_D$ and $V_Q$ be the two dimensional simple representations of $D_4$ and $Q_8$ respectively. Let $1_D$ and $1_Q$ denote their trivial representations. Suppose that there is a tensor equivalence ...
• 8,441
Accepted

### Conjecture of relation between residues of Feynman integrals and mixed Tate motives

1) Counterexamples were found in the paper Brown, Francis; Schnetz, Oliver: "A $K3$ in $\phi^4$". Duke Math. J. 161 (2012), no. 10, 1817–1862. It is now the general feeling that most $\phi^4$-Feynman ...
• 13.9k
Accepted

### Why linearization leads to arithmetization?

I think: The category of varieties over $\mathbb Q$ is already very arithmetic. One reason that the linearization is considered arithmetic is that so much of the tractable arithmetic information is ...
• 122k

### Tannakian Formalism for the Quaternions and Dihedral Group

The categories ${\rm Rep}(Q_8)$ and ${\rm Rep}(D_8)$ are not equivalent as tensor categories. They have the same Grothendieck ring, but they have non equivalent associators. As far as I am aware, it ...
• 3,610
Accepted

• 34.7k
Deligne proved that assuming that $C$ is Tannakian and $K$-linear, where $K$ is an algebraically closed field of characteristic zero, then there is a unique fiber functor from C to $Vec_K$. If you ...