93 research outputs found
On some implications of formalized theories in our life
The formalized theories in which are considered different types of logics give us an easier way of understanding of our own interpretations of the concepts and of the events of life
THE FULFILLED EUCLIDEAN PLANE
The fulfilled euclidean plane is the real projective plane, completed with the infinite point of its infinite line denoted new incidence structure. This is a structure with neighbouring elements, in which the unicity of the line through two distinct points is not assured. This new Geometry is a Smarandacheian structure introduced here which generalizes and unites in the same time: Euclid, Bolyai Lobacewski Gauss and Riemann Geometries
Integral canonical models of unitary Shimura varieties
We prove the existence of integral canonical models of unitary Shimura
varieties in arbitrary unramified mixed characteristic. Errata to [Va1] are
also included.Comment: 27 pages. Accepted (in final form) for publication in Asian J. Mat
Good reductions of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic. Part I
We prove the existence of good smooth integral models of Shimura varieties of
Hodge type in arbitrary unramified mixed characteristic . As a first
application we provide a smooth solution (answer) to a conjecture (question) of
Langlands for Shimura varieties of Hodge type. As a second application we prove
the existence in arbitrary unramified mixed characteristic of integral
canonical models of projective Shimura varieties of Hodge type with respect to
h--hyperspecial subgroups as pro-\'etale covers of N\'eron models; this forms
progress towards the proof of conjectures of Milne and Reimann. Though the
second application was known before in some cases, its proof is new and more of
a principle.Comment: 87 pages. Final version, to appear in Mathematische Nachrichten (most
alignment issues kept loose to match with the layout of the journal
Deformation subspaces of p-divisible groups as formal Lie groups associated to p-divisible groups
Let be an algebraically closed field of characteristic . Let be
a -divisible group over which is not isoclinic. Let \scrD (resp.
\scrD_k) be the formal deformation space of over \Spf(W(k)) (resp. over
\Spf(k)). We use axioms to construct formal subschemes \scrG_k of \scrD_k
that: (i) have canonical structures of formal Lie groups over \Spf(k)
associated to -divisible groups over , and (ii) give birth, via all
geometric points \Spf(K)\to\scrG_k, to -divisible groups over that are
isomorphic to . We also identify when there exist formal subschemes
\scrG of \scrD which lift \scrG_k and which have natural structures of
formal Lie groups over \Spf(W(k)) associated to -divisible groups over
. Applications to Traverso (ultimate) stratifications are included as
well.Comment: 36 pages. To appear in J. Alg. Geo
Surjectivity Criteria for p-adic Representations, Part I
We prove several surjectivity criteria for -adic representations. In
particular, we classify all adjoint and simply connected group schemes over
the Witt ring of a finite field such that the epimorphism
has a section.Comment: 28 page
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