T-motives

Considering a (co)homology theory $\mathbb{T}$ on a base category $\mathcal{C}$ as a fragment of a first-order logical theory we here construct an abelian category $\mathcal{A}[\mathbb{T}]$ which is universal with respect to models of $\mathbb{T}$ in abelian categories. Under mild conditions on the base category $\mathcal{C}$, e.g. for the category of algebraic schemes, we get a functor from $\mathcal{C}$ to ${\rm Ch}({\rm Ind}(\mathcal{A}[\mathbb{T}]))$ the category of chain complexes of ind-objects of $\mathcal{A}[\mathbb{T}]$. This functor lifts Nori's motivic functor for algebraic schemes defined over a subfield of the complex numbers. Furthermore, we construct a triangulated functor from $D({\rm Ind}(\mathcal{A}[\mathbb{T}]))$ to Voevodsky's motivic complexes.Comment: Added reference to arXiv:1604.00153 [math.AG

Effects of Rescattering in (e,e'p) Reactions within a Semiclassical Model

The contribution of rescattering to final state interactions in (e,e'p) cross sections is studied for medium and high missing energies using a semiclassical model. This approach considers two-step processes that lead to the emission of both nucleons. The effects of nuclear transparency are accounted for in a Glauber inspired approach and the dispersion effects of the medium at low energies are included. It is found that rescattering is strongly reduced in parallel kinematics. At high missing energy and momenta, the distortion of the short-range correlated tail of the spectral function is dominated by a rearrangement of that strength itself. In perpendicular kinematics, a further enhancement of the experimental yield is due to strength that is originally in the mean field region. This contribution becomes negligible at large missing momenta.Comment: 10 pages, 9 figures. Minor corrections: improved figures and few comments adde

1-motivic sheaves and the Albanese functor

We introduce n-generated sheaves and n-motivic sheaves, describing completely for n = 0, 1 and proposing a conjecture for n > 1. We then obtain functors L\pi_0 and LAlb on DM_{eff}(k) deriving \pi_0 and Alb. The functor LAlb extends the one constructed (by the second author jointly with B.Kahn) to non-necessarily geometric motives. These functors are then used to define higher N\'eron-Severi groups and higher Albanese sheaves. The latter may be considered as an algebraic avatar of Deligne (co)homology.Comment: 54 pages, fully revised exposition with a new "structure theorem" for 1-motivic sheaves, see Theorem 1.3.10, including finitely presented (or constructible) 1-motivic sheave

Albanese and Picard 1-motives

We define, in a purely algebraic way, 1-motives $Alb^{+}(X)$, $Alb^{-}(X)$, $Pic^{+}(X)$ and $Pic^{-}(X)$ associated with any algebraic scheme $X$ over an algebraically closed field of characteristic zero. For $X$ over \C of dimension $n$ the Hodge realizations are, respectively, $H^{2n-1}(X)(n)$, $H_{1}(X)$, $H^{1}(X)(1)$ and $H_{2n-1}(X)(1-n)$.Comment: 5 pages, LaTeX, submitted as CR Not