Fitting ideals of isotypic parts of even K-groups

On Higher Special Elements ofp-adic Representations

“…In this way we are led to, amongst other things, extend the existing theory of refined Stark conjectures (see Remark 5.6), address a problem explicitly raised by Washington in [38,Remark after Th. 8.2] and by Lang in [20, p. 260] (see §5.2.3), extend and refine the conjectures that are formulated by Castillo and Jones in [10] and by Solomon in [33] (see Remark 5.11), refine the main conjecture formulated by Kurihara and the first and second authors in [5] (see Remark 5.14) and both extend and correct the main result proved by El Boukhari in [15] (see Remark 5.16).…”

“…In this way we are led to, amongst other things, extend the existing theory of refined [10] and by Solomon in [33] (see Remark 5.11), refine the main conjecture formulated by Kurihara and the first and second authors in [5] (see Remark 5.14) and both extend and correct the main result proved by El Boukhari in [15] (see Remark 5.16).…”

“…Remark 5.16. The result of Theorem 5.15 both extends, and clarifies, the main result of El Boukhari in [15]. To explain this, we fix an odd prime p and write H for the maximal subgroup of G of order prime to p and I ℓ for the inertia subgroup in G of each rational prime ℓ.…”

“…The equality in the main result (Theorem 6.5) of [15] is of precisely this form but is obtained under the additional assumptions that m is odd and χ is non-trivial on the intersection of H with the full decomposition subgroup in G of each prime that ramifies in F . In addition, the factor 'Q(0)' that occurs in the statement of [15, Th.…”

On a Gross conjecture over imaginary quadratic fields

“…Their applications in this case are many and touch various subjects in the number theory of higher algebraic K-groups (e.g. [17], [8], [9] and others). In the non-absolute abelian case, Gross's conjecture doesn't provide any particular formula for the definition of these special units.…”