Giada Grossi Kolyvagin’s conjecture and Iwasawa theory

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Let E be a rational elliptic curve and p be an odd prime of good ordinary reduction for E. In 1991 Kolyvagin conjectured that the system of cohomology classes derived from Heegner points on the p-adic Tate module of E over an imaginary quadratic field K is non-trivial. I will talk about joint work with A.Burungale, F.Castella, and C.Skinner, where we prove Kolyvagin's conjecture in the cases where an anticyclotomic Iwasawa Main Conjecture for E/K is known. Moreover, our methods also yield a proof of a refinement of Kolyvagin's conjecture expressing the divisibility index of the Heegner point Kolyvagin system in terms of the Tamagawa numbers of E. One of the proof’s key ingredients, on which I will focus during the talk, is a refinement of the Kolyvagin system argument for (anticyclotomic) twists of E studied by Jan Nekovář. • Giada Grossi (CNRS, University Sorbonne Paris Nord)","styleRuns":[{"startIndex":0,"length":888,"styleRunExtensions":{"styleRunColorMapExtension":{"colorMap":[{"key":"USER_INTERFACE_THEME_DARK","value":4294967295},{"key":"USER_INTERFACE_THEME_LIGHT","value":4279440147}]}},"fontFamilyName":"Roboto"}]},"headerRuns":[{"startIndex":0,"length":888,"headerMapping":"ATTRIBUTED_STRING_HEADER_MAPPING_UNSPECIFIED"}]}},{"itemSectionRenderer":{"contents":[{"messageRenderer":{"text":{"runs":[{"text":"Reacties staan uit. 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