Notiziario Scientifico
Settimana dal 9 al 15 settembre 2013
Martedì 10 settembre 2013
Giovedì 12 settembre 2013
Venerdì 13 settembre 2013
Sabato 14 settembre 2013
Tutte le informazioni relative a questo notiziario devono pervenire
all'indirizzo di posta elettronica
seminari@mat.uniroma1.it,
o nella casella della posta di Luigi Orsina, entro le ore 9 del venerdì
precedente la settimana di pubblicazione.
Ore 11:00, Aula Dal Passo, Università di Roma II
Let G be an reductive algebraic group (for example a special linear group) and let B be a Borel
subgroup (i.e., a maximal closed connected solvable subgroup). The representation theory of G is
closely related to the algebraic geometry of the quotient space G/B. In characteristic 0 this
connection is succinctly summarized by the Borel-Bott-Weil Theorem. This shows in particular that
the cohomology of a line bundle is non-zero in at most one degree and its character is either a Weyl
character or 0. In characteristic p the connection between the representation theory and geometry
still exists and has been extremely useful (in work by Haboush, Andersen, Jantzen and others).
Nevertheless there is no known analogue of the Borel-Bott-Weil Theorem. Earlier work (e.g. that of
Andersen and Humphreys) has focused on the module structure of the cohomology spaces. However,
concentrating only on the character one can get complete information in some low rank cases using
infinitesimal methods. So far the cases worked out completely are G = SL(2) (classical), G = SL(3)
(Donkin), and G = Sp(4) in characteristic2 (Donkin and Geranios). We describe an approach to this
problem using infinitesimal methods and how they may be used to give recursive formulas for the
characters of the cohomology of line bundles in favorable circumstances.
Ore 11:00, Aula Dal Passo, Università di Roma II
Let G be an reductive algebraic group (for example a special linear group) and let B be a Borel
subgroup (i.e., a maximal closed connected solvable subgroup). The representation theory of G is
closely related to the algebraic geometry of the quotient space G/B. In characteristic 0 this
connection is succinctly summarized by the Borel-Bott-Weil Theorem. This shows in particular that
the cohomology of a line bundle is non-zero in at most one degree and its character is either a Weyl
character or 0. In characteristic p the connection between the representation theory and geometry
still exists and has been extremely useful (in work by Haboush, Andersen, Jantzen and others).
Nevertheless there is no known analogue of the Borel-Bott-Weil Theorem. Earlier work (e.g. that of
Andersen and Humphreys) has focused on the module structure of the cohomology spaces. However,
concentrating only on the character one can get complete information in some low rank cases using
infinitesimal methods. So far the cases worked out completely are G = SL(2) (classical), G = SL(3)
(Donkin), and G = Sp(4) in characteristic2 (Donkin and Geranios). We describe an approach to this
problem using infinitesimal methods and how they may be used to give recursive formulas for the
characters of the cohomology of line bundles in favorable circumstances.
Ore 15:10, Biblioteca, Università degli Studi Internazionali, via C.Colombo 200
15:10 Giandomenico Boffi
15:15 Antonio Magliulo, Angelo Guerraggio
15:45 Guido Tortorella Esposito
16:30 Pausa caffè
17:00 Marco Papi
17:45 Antonio Di Cesare
18:30 Dibattito
Ore 9:10, Biblioteca, Università degli Studi Internazionali, via C.Colombo 200
9:10 Introduzione
9:30 Ahmad Naimzada
10:15 Pausa caffè
10:45 Andrea Brandolini
11:30 Dibattito
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invitati a comunicare il proprio indirizzo di posta elettronica a
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