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Apr
9
awarded  Nice Answer
Apr
8
revised What are some geometric / physical / probabilistic interpretations of the Riemann zeta function at integer arguments n ≤ 1?
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Apr
8
comment What are some geometric / physical / probabilistic interpretations of the Riemann zeta function at integer arguments n ≤ 1?
on the "in some sense": the -1/12 in string theory is related to the fact that the discriminant function $\Delta$ is modular of weigth 12. It is this fact which is directly related to the Euler characteristic of the moduli of elliptic curves by a first Chern class argument.
Mar
31
answered What are some geometric / physical / probabilistic interpretations of the Riemann zeta function at integer arguments n ≤ 1?
Mar
29
comment Hodge Decompositions and Gamma Factors of Hasse--Weil L-Functions
Another point: maybe Gamma factors at the Archimedean places are most easily undestood on the automorphic side of the story. I am certainly not an expert of these questions and I hope someone else will say more.
Mar
29
comment Hodge Decompositions and Gamma Factors of Hasse--Weil L-Functions
About the date 1991: from what I understand, the story of the Deninger interpretation is somewhat involved: it is motivated by p-adic Hodge theory and not directly by the usual formulation of Hodge theory.
Mar
29
comment Hodge Decompositions and Gamma Factors of Hasse--Weil L-Functions
The only motivation I see in the paper of Serre is that Gamma factors appear in the known examples (number fields, modular curves...) It would be great if someone could say if Serre had more conceptual motivations, I don't know.
Mar
29
awarded  Nice Question
Mar
28
revised What is the meaning of $(h^{11},h^{21})\to (h^{11}-240,h^{21}+240)$ in Calabi-Yau threefolds?
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Mar
27
comment Hodge Decompositions and Gamma Factors of Hasse--Weil L-Functions
Do you know the work of Deninger "On the \Gamma factors attached to motives", Invent. Math. 104 (1991) 245-261?
Mar
27
answered What is the meaning of $(h^{11},h^{21})\to (h^{11}-240,h^{21}+240)$ in Calabi-Yau threefolds?
Dec
14
answered SU(2) Lefschetz decomposition for cohomology of Riemann surface Jacobian
Nov
25
comment Moduli space of motives vs moduli space of varieties
If I want that my preceding comment makes sense, I should rather say : such that the family of Hodge structures over C admits a connection such that Griffits transversality is satisfied (i.e. one has a "variation of Hodge structures")
Nov
25
comment Moduli space of motives vs moduli space of varieties
related : mathoverflow.net/questions/114847/…
Nov
25
comment Moduli space of motives vs moduli space of varieties
Let H in D be in the "image of motives". Let C a germ of curve in D through H such that the family of Hodge structures over C satisfies Griffits transversality. Is C in the "image of motives"? (In other words, is Griffiths transversality the only obstruction)
Nov
19
awarded  Nice Answer
Nov
2
comment Ext groups of affine scheme
I think the first isom is always true : Ext^n are spaces of extensions and an extension of quasi-coherent sheaves is quasi-coherent. I guess the second iso is not always true even for n=0 if M is not assumed to be of finite presentation because in this case Hom does not always commute with localization, but I don't have an easy counterexample now...
Sep
28
comment Has the conformally field theoretic metric on a Calabi-Yau variety been proved to exist?
Thanks a lot for the nice mathematical reformulation and for the interesting results on the question 2).
Sep
21
comment Has the conformally field theoretic metric on a Calabi-Yau variety been proved to exist?
By the way, the article by Nemeschansky and Sen is rather readable and can be found here : ccdb5fs.kek.jp/cgi-bin/img/allpdf?198605369
Sep
21
comment Has the conformally field theoretic metric on a Calabi-Yau variety been proved to exist?
and likely unpracticable. In fact, I think that my question makes sense by imposing just general conditions on the terms of beta of order greater than one : scalar function globally defined, polynomial in the derivatives of the Kähler potential...Only such properties are used in the article by Nemeschansky and Sen.