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It would be difficult to overestimate the influence and importance
of modular forms, modular curves, and modular abelian varieties in
the development of num- ber theory and arithmetic geometry during
the last fifty years. These subjects lie at the heart of many past
achievements and future challenges. For example, the theory of
complex multiplication, the classification of rational torsion on
el- liptic curves, the proof of Fermat's Last Theorem, and many
results towards the Birch and Swinnerton-Dyer conjecture all make
crucial use of modular forms and modular curves. A conference was
held from July 15 to 18, 2002, at the Centre de Recerca Matematica
(Bellaterra, Barcelona) under the title "Modular Curves and Abelian
Varieties". Our conference presented some of the latest
achievements in the theory to a diverse audience that included both
specialists and young researchers. We emphasized especially the
conjectural generalization of the Shimura-Taniyama conjecture to
elliptic curves over number fields other than the field of rational
numbers (elliptic Q-curves) and abelian varieties of dimension
larger than one (abelian varieties of GL2-type).
Buongiorno Italia is a beginners course in Italian. Based on
authentic conversations and interviews recorded in Italy, it offers
a unique introduction to simple, everyday language. It is now fully
revised in a new edition, including the euro and up-to-date
cultural information about life in Italy. those studying in a
class. Divided into 20 short units, the book contains dialogues,
language notes, information about Italian society, vocabulary and
practice activities. There is also a full reference section,
including answers, grammar notes and a glossary. The audio offers
the chance to develop listening and speaking skills, with real-life
conversations, stage-by-stage pronunciation practice and further
activities.
It would be difficult to overestimate the influence and importance
of modular forms, modular curves, and modular abelian varieties in
the development of num- ber theory and arithmetic geometry during
the last fifty years. These subjects lie at the heart of many past
achievements and future challenges. For example, the theory of
complex multiplication, the classification of rational torsion on
el- liptic curves, the proof of Fermat's Last Theorem, and many
results towards the Birch and Swinnerton-Dyer conjecture all make
crucial use of modular forms and modular curves. A conference was
held from July 15 to 18, 2002, at the Centre de Recerca Matematica
(Bellaterra, Barcelona) under the title "Modular Curves and Abelian
Varieties". Our conference presented some of the latest
achievements in the theory to a diverse audience that included both
specialists and young researchers. We emphasized especially the
conjectural generalization of the Shimura-Taniyama conjecture to
elliptic curves over number fields other than the field of rational
numbers (elliptic Q-curves) and abelian varieties of dimension
larger than one (abelian varieties of GL2-type).
Buongiorno Italia! is the highly successful course for beginners
learning Italian. Whether learning at home or in a class, you will
learn to use and understand basic colloquial Italian in a wide
range of everyday situations. You can gain valuable insights into
modern Italian culture, and extended reading material in Italian
will enhance your learning experience, introducing more advanced
language and specialist topics. Focusing on listening, reading,
writing and speaking skills, Buongiorno Italia! will help you reach
the equivalent of a first qualification, such as GCSE. The Language
CD pack contains 1 Book and 3 Audio CDs.
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