The fundamental group scheme of a non-reduced scheme

Antei, Marco

doi:10.1016/j.bulsci.2011.02.002

Cited by 2 publications

(3 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [2], the first author made an attempt to construct FGS in this setting by showing that the category of finite pointed Galois torsors (see Definition 2.1) is cofiltered. Unfortunately proof in [2] contains a mistake, in fact here we give an actual counterexample to his claim (cf. Example 2.3).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The pseudo-fundamental group scheme

Antei

Dey

2019

Journal of Algebra

Self Cite

View full text Add to dashboard Cite

Let X be any scheme defined over a Dedekind scheme S with a given section x ∈ X(S). We prove the existence of a pro-finite S-group scheme ℵ(X, x) and a universal ℵ(X, x)-torsor dominating all the pro-finite pointed torsors over X. Though ℵ(X, x) may not be unique in general it still can provide useful information in order to better understand X. In a similar way we prove the existence of a pro-algebraic S-group scheme ℵ alg (X, x) and a ℵ alg (X, x)-torsor dominating all the pro-algebraic and affine pointed torsors over X. The case where X → S has no sections is also considered.Mathematics Subject Classification. Primary: 14L15, 14G17. Secondary: 11G99.

show abstract

Section: Introductionmentioning

confidence: 99%

“…Example 2.3). In this paper we keep the same idea of [2] i.e. considering Galois torsors instead of taking all of them but in a larger category of profinite torsors.…”

Section: Introductionmentioning

confidence: 99%

The pseudo-fundamental group scheme

Antei

Dey

2019

Journal of Algebra

Self Cite

View full text Add to dashboard Cite

show abstract

“…Over any base scheme S a pointed G-torsor Y → X over S is said to be quotient if X has a fundamental group scheme π 1 (X, x) (cf. for instance[4], where the existence of the fundamental group scheme is studied) and the canonical morphism of S-group schemes π 1 (X, x) → G is faithfully flat…”

mentioning

confidence: 99%

Extension of finite solvable torsors over a curve

Antei¹

2012

manuscripta math.

Self Cite

View full text Add to dashboard Cite

Let R be a discrete valuation ring with fraction field K and with algebraically closed residue field of positive characteristic p. Let X be a smooth fibered surface over R with geometrically connected fibers endowed with a section x ∈ X(R). Let G be a finite solvable K-group scheme and assume that either |G| = p n or G has a normal series of length 2. We prove that every quotient pointed G-torsor over the generic fiber X η of X can be extended to a torsor over X after eventually extending scalars and after eventually blowing up X at a closed subscheme of its special fiber X s .Mathematics Subject Classification: 14H30, 14L15.

show abstract

The fundamental group scheme of a non-reduced scheme

Abstract: We extend the definition of fundamental group scheme to non reduced schemes over any connected Dedekind scheme. Then we compare the fundamental group scheme of an affine scheme with that of its reduced part.Mathematics Subject Classification. Primary: 14L15. Secondary: 14G17.

Cited by 2 publications

References 11 publications

The pseudo-fundamental group scheme

The pseudo-fundamental group scheme

Extension of finite solvable torsors over a curve

Contact Info

Product

Resources

About