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CTNT 2018 - "Function Field Arithmetic" (Lecture 2) by Christelle Vincent

Drinfeld modules and arithmetic in the function fields Dinesh S. Oxford Academic.

Function field arithmetic

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Function Field Arithmetic

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You could not be signed in. Sign In Forgot password? Springer Professional. Back to the search result list. This lecture series introduces in the first part a cohomological theory for varieties in positive characteristic with finitely generated rings of this characteristic as coefficients developed jointly with Richard Pink.

Ideal arithmetic and infrastructure in purely cubic function fields

In the second part various applications are given. Having succumbed to the requests of the organisers of the Research Programme on Function Field Arithmetic that was held in at the CRM in Barcelona, we present here a survey of some recent results concerning certain aspects of the Iwasawa theory of varieties over finite fields. The Binomial Theorem has played a crucial role in the development of mathematics, algebraic or analytic, pure or applied.

It was very important in the development of calculus, in a variety of ways, and has certainly been as important in the development of number theory.

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On the other hand although their study were originally undertaken in order to make advance on the above-mentioned conjectures, now it is a discipline on its own, an extremely rich theory which have a counterpart for every object which is studied by classical number theory, including modular varieties and modular forms, L- and Gamma-functions, Galois representations and Hodge theory, Bernoulli numbers and transcendence results and which often closely mirrors, but sometimes tantalising diverges from the arithmetic of number fields.

Moreover very often the state of art in the arithmetic of function fields is far more advanced than in the case of number fields, hence the area still serves its role as an important testing ground for the major conjectures of number theory. The area also has deep connections to representation theory, algebraic and arithmetic geometry, group theory and even combinatorics. It is very natural to expect that many major results in this area are still to be discovered.


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Some of the leading experts have already accepted to speak and attending Ph. The other aim of the workshop is to stimulate discussion among its participants and further research in this exciting area. Workshop on function field arithmetic.