Summary: Let \(S(g,1)\) be a connected, compact, oriented surface of genus \(g\), with one boundary component and Mod\((g,1)\) its mapping class group. Let \(p\) be an integer, either equal to 0, or a prime \(\geq 2\). We construct a central \(p\)-filtration of Mod\((g,1)\), denoted \(\{M(k, p): k \in\mathbb N^* = \mathbb N-\{0\}\}\), generalizing the Johnson filtration (which corresponds to \(p =0\)) such that \(M(1, g) =\text{Mod}(g,1)\), \(M(k, p) M(k +1, p)\) \((k\geq 2)\) is a finite dimensional \(\mathbb Z/p\mathbb Z\)-vector space and \(M(2,p)\) is the Torelli group \(\pmod p\) (e.g. the subgroup of Mod\((g,1)\) of homeomorphisms which induce the identity on \(H_1(S(g,1)\); \(\mathbb Z/p\mathbb Z))\). We announce the following results: the Torelli group \(\pmod p\) is generated by the usual Torelli group and the \(p\)-th powers of all Dehn twists. We compute the abelianization of the Torelli group \(\pmod p\), up to finite 2-torsion. Any \(\mathbb Q\)-homology sphere \(\Sigma^3\) is obtained by gluing two handlebodies by an element of the Torelli group \(\pmod p\), for any prime \(p\geq 3\) dividing \((n-1)\), where \(n\) is the cardinal of \(H_1(\Sigma^3;\mathbb Z)\). Finally we propose a conjectural invariant for these \(\mathbb Q\)-homology spheres.