Skip to main content

All Questions

7 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
12 votes
0 answers
811 views

Number field analog of Artin-Tate $\Rightarrow$ BSD?

What is the difference between the alternating product of the Hasse-Weil $L$-functions of the generic fiber of an arithmetic scheme $X\to\text{Spec}(\mathbf{Z})$ and the zeta function of $X$? (each ...
user avatar
8 votes
0 answers
603 views

A Generalization of the Tate-Shafarevich/Tate/Fontaine-Mazur Conjectures

Let $A$ be an abelian variety over a number field $k$. The Tate-Shafarevich conjecture says that the Tate-Shafarevich group of $A$ is finite. A weakening of this conjecture states that the $\ell$-...
David Corwin's user avatar
  • 15.4k
7 votes
0 answers
444 views

Status of the conjectured vanishing of Bloch-Kato H^2

There is a folklore conjecture that $\operatorname{Ext}^2$ vanishes in the category of geometric $p$-adic Galois representations (i.e. representations that are unramified almost everywhere and de Rham ...
David Corwin's user avatar
  • 15.4k
5 votes
0 answers
210 views

Motivic $L$-functions came from automorphic representations

Langlands in his 1978 ICM talk made a conjecture that all motivic $L$-functions should arise as automorphic $L$-functions. A part of this conjecture, namely for some Hasse-Weil $\zeta$ functions is a ...
coLaideronnette's user avatar
5 votes
0 answers
834 views

Motivic Galois group and Shimura varieties

Hi, Suppose that one has a Shimura variety $Sh(G,X)$ where $(G,X)$ is the corresponding Shimura datum and suppose that it can be interpreted as a moduli space of motives (e.g. PEL type Shimura ...
unknown's user avatar
  • 647
3 votes
0 answers
143 views

A Galois equivariant Weil cohomology theory with coefficients in the rational numbers and a variation of the Tate/Hodge conjecture

A well-known example of Serre shows that there can be no Weil cohomology theory with $\mathbb Q$ coefficients for schemes over $\mathbb F_{p^2}$. However, this example is no obstruction to a Weil ...
Asvin's user avatar
  • 7,746
3 votes
0 answers
128 views

On Abhyankar's results cited in a paper of Manin titled "Correspondences, Motifs and Monoidal Transformations"

Consider the following from this paper "Correspondences, Motifs and Monoidal Transformations" of Manin here. Theorem. Nonsingular three-dimensional projective unirational varieties $V$ over ...
user100749's user avatar