CMI Workshop:
SAGE

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The goal of this workshop is to study explicit computation with mathematical objects in connection with the Birch and Swinnerton-Dyer conjecture, including Mordell-Weil groups, complex and p-adic L-series, Heegner points, Kolyvagin classes, Stark-Heegner points, Iwasawa modules, and analogous objects for elliptic curves over function fields. We also intend to create and discuss practical implementations of associated algorithm in the open source computer software Sage

. Topics may include:

• Computing Heegner points on elliptic curves and abelian varieties
• Computing Stark-Heegner points
• Equidistribution of Heegner points
• High precision computation of complex L-series
• Computing p-adic L-series
• Verifying the BSD conjecture for specific elliptic curves and abelian varieties
• Universal norms and Mordell-Weil "shadow lines"
• Computing p-adic heights and p-adic regulators
• Splitting behavior of Galois cohomology classes over solvable extensions