bio | website | andreasholmstrom.org |
---|---|---|
location | Norway | |
age | ||
visits | member for | 4 years, 9 months |
seen | Jun 12 at 1:50 | |
stats | profile views | 2,117 |
Interested in homotopical arithmetic geometry.
Jul 14 |
awarded | Guru |
Jul 2 |
awarded | Curious |
Jun 11 |
awarded | Good Question |
Jun 8 |
comment |
What (if anything) unifies stable homotopy theory and Grothendieck's six functors formalism?
In addition to the brief answer below, maybe these slides could be of interest: homotopical.files.wordpress.com/2014/06/ctsaghandout.pdf |
Jun 8 |
comment |
Local factors of Hasse-Weil zeta function - what do they have in common?
Ah, I see. Thanks Antoine, and Felipe! |
Jun 8 |
revised |
What (if anything) unifies stable homotopy theory and Grothendieck's six functors formalism?
edited body |
Jun 8 |
answered | What (if anything) unifies stable homotopy theory and Grothendieck's six functors formalism? |
Jun 7 |
accepted | Local factors of Hasse-Weil zeta function - what do they have in common? |
Jun 7 |
comment |
Local factors of Hasse-Weil zeta function - what do they have in common?
Felipe, how does the functional equation help here? |
Jun 7 |
comment |
Local factors of Hasse-Weil zeta function - what do they have in common?
Great answer, thank you! |
Jun 7 |
comment |
Local factors of Hasse-Weil zeta function - what do they have in common?
Sorry Felipe (and David), I realise my comment came across as overly disapproving. That was not my intention. |
Jun 7 |
comment |
Local factors of Hasse-Weil zeta function - what do they have in common?
David, I get the feeling you didn't read the question, but maybe I didn't state it very clearly. Of course the Betti numbers govern the degrees of these polynomials, and of course the Weil conjectures give us even more information, in terms of the Riemann hypothesis which determines the absolute value of the numbers $\alpha_{ij}$. The question is whether one in general can get more precise information about how these polynomials vary in a flat family. |
Jun 6 |
revised |
Local factors of Hasse-Weil zeta function - what do they have in common?
Added reference to comments on point counts. |
Jun 6 |
comment |
Local factors of Hasse-Weil zeta function - what do they have in common?
I guess part of what I ask is whether one in general can describe the coefficients in terms of point counts, and if so, how far up in the tower of fields above F_p would you have to perform such point counts in order to describe the coefficients? |
Jun 6 |
comment |
Local factors of Hasse-Weil zeta function - what do they have in common?
They numbers a_p are the same in the sense that they all are given by counting points in the fiber. They are also the same in the sense that they are all given as Frobenius traces of the same global object. Does that make the question more sensible? |
Jun 6 |
comment |
Local factors of Hasse-Weil zeta function - what do they have in common?
David, thanks for the comments! Sure, your points about Betti numbers and a_p being there by definition are valid. Let me try to reformulate the question slightly: What does Poincare duality say about the zeta coefficients of a genus 2 curve? Or a K3 surface, or a cubic threefold? In all cases, the degree of the polynomial factors will of course be governed by the Betti number, but I'm looking for a more concrete description of each coefficient, maybe in terms of point counts in the fibers. |
Jun 6 |
comment |
Local factors of Hasse-Weil zeta function - what do they have in common?
Qiaochu, the Weil conjectures say a lot about the local factors, but they don't say anything about how they vary in a flat family. |
Jun 6 |
asked | Local factors of Hasse-Weil zeta function - what do they have in common? |
Oct 14 |
awarded | Yearling |
Sep 21 |
awarded | Famous Question |