Matemática
https://hdl.handle.net/10669/280
Mon, 29 Nov 2021 09:54:27 GMT2021-11-29T09:54:27ZNori fundamental gerbe of essentially finite covers and Galois closure of towers of torsors
https://hdl.handle.net/10669/79845.2
Nori fundamental gerbe of essentially finite covers and Galois closure of towers of torsors
We prove the existence of a Galois closure for towers of torsors under finite group schemes over a proper, geometrically connected and geometrically reduced algebraic stack X over a field k. This is done by describing the Nori fundamental gerbe of an essentially finite cover of X. A similar result is also obtained for the S -fundamental gerbe.
Tue, 01 Jan 2019 00:00:00 GMThttps://hdl.handle.net/10669/79845.22019-01-01T00:00:00ZModels of torsors and the fundamental group scheme
https://hdl.handle.net/10669/85333
Models of torsors and the fundamental group scheme
Given a relative faithfully
at pointed scheme over the spectrum
of a discrete valuation ring X !S, this paper is motivated by the study of
the natural morphism from the fundamental group scheme of the generic ber
X to the generic ber of the fundamental group scheme of X. Given a torsor
T !X under an a ne group scheme G over the generic ber of X, we address
the question of nding a model of this torsor over X, focusing in particular on
the case where G is nite. We provide several answers to this question, showing
for instance that, when X is integral and regular of relative dimension 1, such a
model exists on some model X0 of X obtained by performing a nite number
of N eron blowups along a closed subset of the special ber of X. Furthermore,
we show that when G is etale, then we can nd a model of T !X under the
action of some smooth group scheme. In the rst part of the paper, we show
that the relative fundamental group scheme of X has an interpretation as the
Tannaka Galois group of a Tannakian category constructed starting from the
universal torsor.
Mon, 01 Jan 2018 00:00:00 GMThttps://hdl.handle.net/10669/853332018-01-01T00:00:00ZAnaliticity of the Lyapunov exponents of random products of quasi-periodic cocycles
https://hdl.handle.net/10669/85293
Analiticity of the Lyapunov exponents of random products of quasi-periodic cocycles
We show that the top Lyapunov exponent LE(p) associated with a random product of quasi-periodic cocycles depends real analytically on the transition probabilities p whenever LE(p) is simple. Moreover if the spectrum at p is simple (all Lyapunov exponents having multiplicity one ) then all Lyapunov exponents depend real analytically on p.
Mon, 01 Nov 2021 00:00:00 GMThttps://hdl.handle.net/10669/852932021-11-01T00:00:00ZEquilibrium states for maps isotopic to Anosov
https://hdl.handle.net/10669/85279
Equilibrium states for maps isotopic to Anosov
In this work we address the problem of existence and uniqueness (finiteness) of ergodic equilibrium states for partially hyperbolic diffeomorphisms isotopic to Anosov on T4, with two-dimensional center foliation. To do so we propose to study the disintegration of measures along one-dimensional subfoliations of the center bundle. Moreover, we obtain a more general result characterizing the disintegration of ergodic measures in our context.
Fri, 01 Jan 2021 00:00:00 GMThttps://hdl.handle.net/10669/852792021-01-01T00:00:00Z