Ogus realization of 1-motives

After introducing the Ogus realization of 1-motives we prove that it is a fully faithful functor. More precisely, following a framework introduced by Ogus, considering an enriched structure on the de Rham realization of 1-motives over a number field, we show that it yields a full functor by making use of an algebraicity theorem of Bost

Greenberg algebras and ramified Witt vectors

Let  be a complete discrete valuation ring of mixed characteristic and with finite residue field k. We study a natural morphism r: R_O→W_{O,k} between the Greenberg algebra of O and the special fiber of the scheme of ramified Witt vectors over O. It is a universal homeomorphism with proinfinitesimal kernel that can be explicitly described in some cases

Remarks on 1-motivic sheaves

category of 1-motives with torsion t M1 in [4] as well as the construction of the category of 1-motivic sheaves Shv1 in [3] to perfect fields (without inverting the exponential characteristic). We extend a result in [3] showing that t M1 and Shv1 have equivalent bounded derived categories. Over a field of characteristic zero, the previous constructions work also for Laumon 1-motives, i.e., allowing additive factors and formal k-groups. 1

Universal extension crystals of 1-motives and applications

We use the crystalline nature of the universal extension of a 1-motive to define a canonical Gauss\u2013Manin connection on the de Rham realization of . As an application we provide a construction of the so-called Manin map from a motivic point of view

Disegnando somme esponenziali

L'articolo rappresenta un'unit\ue0 didattica per avvicinare i ragazzi della scuola superiore alla geometria del piano complesso. Attraverso alcuni esempi di crescente complessit\ue0 si mostra come disegnare poligonali associate a somme esponenziali

Canonical Witt formal scheme extensions and p-torsion groups

We study the nth arithmetic jet space of the p-torsion subgroup attached to a smooth commutative formal group scheme. We show that the nth jet space above fits in the middle of a canonical short exact sequence between a power of the formal scheme of Witt vectors of length n and the p-torsion subgroup we started with. This result generalizes a result of Buium on roots of unity

On deformations of 11-motives

According to a well-known theorem of Serre and Tate, the innitesimal deformation theory of an abelian variety in positive characteristic is equivalent to the innitesimal deformation theory of its Barsotti–Tate group. We extend this result to-motives

Corrigendum: Magnitude assessment of adult neurogenesis in the octopus vulgaris brain using a flow cytometry-based technique (Frontiers in Physiology (2018) 9 (1050) DOI: 10.3389/fphys.2018.01050)

In the original article, there was a mistake in Figure 3 as published. The incorrect image was used. The corrected Figure 3 appears below. (Figure Presented). The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way. The original article has been updated. Conflict of Interest Statement The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest