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Comparison between the fundamental group scheme of a relative scheme and that of its generic fiber

Marco Antei (2010)

Journal de Théorie des Nombres de Bordeaux

We show that the natural morphism ϕ : π 1 ( X η , x η ) → π 1 ( X , x ) η between the fundamental group scheme of the generic fiber X η of a scheme X over a connected Dedekind scheme and the generic fiber of the fundamental group scheme of X is always faithfully flat. As an application we give a necessary and sufficient condition for a finite, dominated pointed G -torsor over X η to be extended over X . We finally provide examples where ϕ : π 1 ( X η , x η ) → π 1 ( X , x ) η is an isomorphism.

Comparison theorems between algebraic and analytic De Rham cohomology (with emphasis on the p -adic case)

Yves André (2004)

Journal de Théorie des Nombres de Bordeaux

We present a panorama of comparison theorems between algebraic and analytic De Rham cohomology with algebraic connections as coefficients. These theorems have played an important role in the development of 𝒟 -module theory, in particular in the study of their ramification properties (irregularity...). In part I, we concentrate on the case of regular coefficients and sketch the new proof of these theorems given by F. Baldassarri and the author, which is of elementary nature and unifies the complex...

Comparison theorems for Gromov–Witten invariants of smooth pairs and of degenerations

Dan Abramovich, Steffen Marcus, Jonathan Wise (2014)

Annales de l’institut Fourier

We consider four approaches to relative Gromov–Witten theory and Gromov–Witten theory of degenerations: J. Li’s original approach, B. Kim’s logarithmic expansions, Abramovich–Fantechi’s orbifold expansions, and a logarithmic theory without expansions due to Gross–Siebert and Abramovich–Chen. We exhibit morphisms relating these moduli spaces and prove that their virtual fundamental classes are compatible by pushforward through these morphisms. This implies that the Gromov–Witten invariants associated...

Compatibility of the theta correspondence with the Whittaker functors

Vincent Lafforgue, Sergey Lysenko (2011)

Bulletin de la Société Mathématique de France

We prove that the global geometric theta-lifting functor for the dual pair ( H , G ) is compatible with the Whittaker functors, where ( H , G ) is one of the pairs ( S 𝕆 2 n , 𝕊 p 2 n ) , ( 𝕊 p 2 n , S 𝕆 2 n + 2 ) or ( 𝔾 L n , 𝔾 L n + 1 ) . That is, the composition of the theta-lifting functor from H to G with the Whittaker functor for G is isomorphic to the Whittaker functor for H .

Complementi di sottospazi e singolarità coniche

Claudio Procesi (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Discuterò una costruzione geometrica, fatta insieme a De Concini, di una modificazione di una configurazione di sottospazi che trasforma i sottospazi in un divisore a incroci normali. Inoltre nel caso di iperpiani questa costruzione è legata alla generalizzazione della equazione di Kniznik-Zamolodchikov ed alla teoria dei nodi, per i sistemi di radici produce dei modelli particolarmente interessati.

Complete arcs arising from a generalization of the Hermitian curve

Herivelto Borges, Beatriz Motta, Fernando Torres (2014)

Acta Arithmetica

We investigate complete arcs of degree greater than two, in projective planes over finite fields, arising from the set of rational points of a generalization of the Hermitian curve. The degree of the arcs is closely related to the number of rational points of a class of Artin-Schreier curves, which is calculated by using exponential sums via Coulter's approach. We also single out some examples of maximal curves.

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