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SUMMARY:Francesco Battistoni (Universite de Framche-Comte)
DTSTART:20210615T123000Z
DTEND:20210615T130000Z
DTSTAMP:20260423T035919Z
UID:POINT/35
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/POINT/35/">O
 n elliptic curves over $\\mathbb{Q}(T)$ and their ranks</a>\nby Francesco 
 Battistoni (Universite de Framche-Comte) as part of POINT: New Development
 s in Number Theory\n\n\nAbstract\nWe consider elliptic curves over $\\math
 bb{Q}(T)$ admitting Weierstrass model with coefficients being polynomials 
 of small degree\, so that they are rational elliptic surfaces. In joint wo
 rk with Sandro Bettin and Christophe Delaunay\, we apply Nagao's formula i
 n order to detect the value of their ranks: this approach is orthogonal to
  other geometric investigations\, and gives the values of the ranks by loo
 king at purely algebraic properties like the factorization of some integer
  polynomials. We also prove that\, whenever restricting to some specific f
 amilies of curves\, the generic curve in these families has rank $0$.\n
LOCATION:https://researchseminars.org/talk/POINT/35/
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