Elliptic Curves and Modular Forms in Arithmetic Geometry
Description
This book arises from the conference "Elliptic Curves and Modular Forms in Arithmetic Geometry, Celebrating Massimo Bertolini's 60th birthday" held in Milano in September 2022. Massimo Bertolini is one of the most influential number theorists of the last 30 years, whose results and ideas have been a source of inspiration for many mathematicians working in the fascinating area of the Birch and Swinnerton-Dyer conjecture, a Millennium Problem of the Clay Institute. The beauty of the subject, combined with the deep mathematics involved, attracts some of the most brilliant mathematicians in all the world. The book of Massimo Bertolini opened the way to study these problems, using several different techniques, especially of p-adic nature, and is recognized as a leading mathematician in this area. Because of the special position of Massimo in this area of number theory, many influential mathematicians attended the conference in Milano and the Summer School in Essen in his honor on the occasion of his 60th birthday.
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Ashay a. Burungale, shinichi kobayashi and kazuto ota, on the tate-shafarevich groups of cm elliptic curves over anticyclotomic zp-extensions at inert primes. Francesc castella, nonvanishing of generalised kato classes and iwasawa main conjectures.- henri darmon and alice pozzi, flach classes and generalised hecke eigenvalues.- samit dasgupta, on constructing extensions of residually isomorphic characters.- christopher deninger and michael wibmer, on the proalgebraic fundamental group of topological spaces and amalgamated products of affine group schemes.- michele fornea and lennart gehrmann, non-archimedean plectic jacobians.- francesca gatti and victor rotger, a p-adic gross-zagier formula for the triple p-adic l-function at non-crystalline points.- chan-ho kim, on the anticyclotomic mazur-tate conjecture for elliptic curves with supersingular reduction.- daniel kriz, the bertolini-darmon-prasanna p-adic l-function via qdr-expansions.- yifeng liu, anticyclotomic p-adic l-functions for rankin-selberg product.- david loeffler, robert rockwood, and sarah livia zerbes, spherical varieties and p-adic families of cohomology classes.- marco adamo seveso, reciprocity laws for generalized heegner classes.- matteo tamiozzo, congruences of modular forms and modularity of tate-shafarevich classes.