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Solving cubic equations in two variables
(Irish Mathematical Society, 2007)
After recalling a geometric construction of all Pythagorean triples of integers, the same idea is applied to find rational solutions of cubic equations in two variables. This leads to the definition of the Mordell-Weil ...
Derived categories of irreducible projective curves of arithmetic genus one
(Cambridge Journals, 2006)
We investigate the bounded derived category of coherent
sheaves on irreducible singular projective curves of arithmetic
genus one. A description of the group of exact auto-equivalences
and the set of all t-structures ...
On a relative Fourier-Mukai transform on genus one fibrations
(Springer, 2006)
We study relative Fourier-Mukai transforms on genus
one fibrations with section, allowing explicitly the total space of
the fibration to be singular and non-projective. Grothendieck duality
is used to prove a ...
Ireland's participation in the 50th international mathematical olympiad
(Irish Mathematical Society, 2009)
The 50th International Mathematical Olympiad (IMO) took place in Bremen (Germany) from 12th July until 22nd July 2009. With 565 participants (59 of whom were girls) from 104 countries, this was the IMO with the largest ...
Elliptic curves – an introduction
(Irish Mathematical Society, 2007)