Weierstrass semigroups and Galois module structure of spaces of holomorphic differentials of curves
72 pages
English

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Weierstrass semigroups and Galois module structure of spaces of holomorphic differentials of curves

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72 pages
English
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Description

Weierstrass semigroups, Galois module structure of holomorphic differentials and applications S. Karanikolopoulos A. Kontogeorgis March 15, 2011

  • ramification filtration

  • deformation theory

  • motivation examples

  • weierstrass semigroups

  • n? ?p

  • defined over

  • g0 ≥

  • natural numbers

  • called pole


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Nombre de lectures 7
Langue English

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Weierstrasssemigroups,GaloismodulestructureofholomorphicdifferentialsandapplicationsS.KaranikolopoulosA.KontogeorgisMarch15,2011
UnivAimofthistalkWeierstrasssemigroupsandramificationfiltrationMotivationExamplesXisaprojectivenonsingularcurveofgenusg2definedoveranalgebraicalyclosedfieldofpositivecharacteristic.WewilldenotethefunctionfieldofXbyF.TheautomorphismgroupofFwillbedenotedbyGanditisafinitegroup..1.2.3resiytoWeierstrasssemigroupsG-modulestructureofpolydifferentialsDeformationtheoryofcurveswithautomorphismsftheAgeaenUnivresiytoftAhnes2/28
WeierstrasssemigroupsandramificationfiltrationMotivationExamplesWeierstrasssemigroupsandramificationfiltration
Univ.1.2resiytoWeierstrasssemigroupsWeierstrasssemigroupsandramificationfiltrationMotivationExamplesTheWeierstrasssemigroupΣPattheplacePofFisthesubsemigroupofthenaturalnumbersthatconsistsofallnumbersiNsuchthatthereisanfFwith(f)=iP.AllnumbersintheWeierstrasssemigroupatParecalledpolenumbers.ThesetNΣPisfiniteandconsistsofgelements.TheelementsofNΣParecalledgaps.Allgapsare2g1.ftheAgeaenUnivresityoftAhnes4/28
Univ.1.2resiytoRamificationFiltrationWeierstrasssemigroupsandramificationfiltrationMotivationExamplesG(P)={gG:g(P)=g}.ThegroupGadmitsthefollowingramificationfiltrationG0G1==Gi1>Gi1+1==Gi2>Gi2+1==Gs>{1}.LettbealocaluniformizeratP.ThegroupsGiaredefinedbyGi={gG(P):vP(g(t)t)i+1}.ftheAgeaenUnivresiytoftAhnes5/28
:miARelateUniversityoftheAegeanRelationsWeierstrasssemigroupsandramificationfiltrationMotivationExamplesramificationfiltrationdnaehtWeierstrasssemigroup.UniversityofAthens–6/28
UnivRelationsWeierstrasssemigroupsandramificationfiltrationMotivationExamplesAim:RelateramificationfiltrationandtheWeierstrasssemigroup.Letmbethesmalerpolenumbernotdivisiblebyp.ConsiderthespaceL(mP),andfixabase.ThereisfaithfulrepresentationofresiytoftheAgeaenρ:G1(P)L(mP).UnivresiytoftAhnes6/28
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