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Elementary introduction to representable functors and Hilbert schemes

Stein Strømme (1996)

Banach Center Publications

The purpose of this paper is to define and prove the existence of the Hilbert scheme. This was originally done by Grothendieck in [4]. A simplified proof was given by Mumford [11], and we will basically follow that proof, with small modifications.

Elements of large order on varieties over prime finite fields

Mei-Chu Chang, Bryce Kerr, Igor E. Shparlinski, Umberto Zannier (2014)

Journal de Théorie des Nombres de Bordeaux

Let 𝒱 be a fixed algebraic variety defined by m polynomials in n variables with integer coefficients. We show that there exists a constant C ( 𝒱 ) such that for almost all primes p for all but at most C ( 𝒱 ) points on the reduction of 𝒱 modulo p at least one of the components has a large multiplicative order. This generalises several previous results and is a step towards a conjecture of B. Poonen.

Elliptic cohomologies: an introductory survey.

Guillermo Moreno (1992)

Publicacions Matemàtiques

Let α and β be any angles then the known formula sin (α+β) = sinα cosβ + cosα sinβ becomes under the substitution x = sinα, y = sinβ, sin (α + β) = x √(1 - y2) + y √(1 - x2) =: F(x,y). This addition formula is an example of "Formal group law", which show up in many contexts in Modern Mathematics.In algebraic topology suitable cohomology theories induce a Formal group Law, the elliptic cohomologies are the ones who realize the Euler addition formula (1778): F(x,y) =: (x √R(y) + y √R(x)/1 - εx2y2)....

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