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Showing 1 to 5 of 5 for “"main conjecture"”.
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Iwasawa theory for tensor products of Hilbert modular forms
The main conjecture of Iwasawa theory bridges two seemingly disjoint areas of mathematics: arithmetic and analysis. In particular, it provides a deep connection between the p-adic L-function which interpolates critical values of the complex L-series, and the Selmer group which is an important …
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Iwasawa theory for modular forms at supersingular primes
… level of f. We study a reformulation of Kato's main conjecture for f over the Zp-cyclotomic extension of Q. In particular, we generalise Kobayashi's main conjecture on p-supersingular elliptic curves over Q with a_p=0, which asserts that Pollack's p-adic L-functions generate the characteristic …
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Iwasawa theory over solvable three-dimensional p-adic Lie extensions
… is neatly encoded in the so-called "Iwasawa Main Conjecture". Classically the Main Conjecture (as formulated by Iwasawa himself) involved the behaviour of ideal class groups over cyclotomic Zp-extensions, and related this to the Kubota-Leopoldt p-adic zeta-function. During the last two …
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On the main conjectures of Iwasawa theory for certain elliptic curves with complex multiplication
The conjecture of Birch and Swinnerton-Dyer is unquestionably one of the most important open problems in number theory today. Let $E$ be an elliptic curve defined over an imaginary quadratic field $K$ contained in $\mathbb{C}$, and suppose that $E$ has complex multiplication by the ring of integers …
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Proper decompositions of finitely presented groups
… after the counter-example given here to the main conjecture of A.N.Bartholomew's Proper Decompositions Of Finitely Presented Groups (1987), that the sum of two tracks giving trivial decompositions gives a trivial decomposition itself, was discovered. A proof is given using Bass-Serre theory …