François Brunault

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7,620 reputation
11845
bio website perso.ens-lyon.fr/…
location Lyon
age 35
visits member for 4 years, 2 months
seen Nov 10 '13 at 12:21

I am a number theorist working at the École normale supérieure de Lyon in France. My research interests are elliptic curves, L-functions and zeta functions, especially the study of their special values (conjectures by Beilinson, Bloch, Kato, Zagier...).


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awarded  Curious
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awarded  Popular Question
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awarded  Yearling
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awarded  Popular Question
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awarded  Nice Question
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awarded  Notable Question
Nov
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awarded  Nice Answer
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awarded  Good Answer
Nov
10
revised calculate function from its divizor
Updated link
Oct
31
comment calculate function from its divizor
Dear Hicham, I edited my answer to give the link to the Pari/GP script.
Oct
31
revised calculate function from its divizor
Added link to Pari/GP script.
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25
awarded  ag.algebraic-geometry
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25
awarded  nt.number-theory
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25
awarded  Revival
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awarded  Pundit
Jun
24
answered On Deligne's determinant of motives
Jun
19
comment modularity of elliptic curves with cm
Note that if $\operatorname{Res}_{F/\mathbf{Q}} E$ appear inside $J_1(N)$ over $\mathbf{Q}$ then $E$ itself appears inside $J_1(N)$ over $F$. So in this case you can find a modular parametrization $X_1(N) \to E$ which is defined over $F$.
Jun
19
comment modularity of elliptic curves with cm
What is true is that every elliptic curve over $\overline{\mathbf{Q}}$ with CM by $K$ is isomorphic over $\overline{\mathbf{Q}}$ to a $K$-curve (a curve which is isogenous over $\overline{\mathbf{Q}}$ to all its $\operatorname{Gal}(\overline{\mathbf{Q}}/K)$-conjugates), see Wortmann's article and the references.
Jun
19
comment modularity of elliptic curves with cm
In the last sentence, I meant "isomorphic over $\overline{\mathbf{Q}}$"...
Jun
19
comment modularity of elliptic curves with cm
There is a nice article where Shimura's result is generalized for a wider class of CM elliptic curves, see S. Wortmann, *Generalized Q-curves and factors of $J_1(N)$* dx.doi.org/10.1007/BF02940901 These CM elliptic curves are sometimes called of Shimura type. I'm not sure but I think these are exactly the CM elliptic curves whose restriction of scalars appear inside $J_1(N)$ over $\mathbf{Q}$. Moreover, every CM elliptic curve is isomorphic over $\mathbf{Q}$ to a curve of Shimura type.