Inflyatsiya-cheklovning aniq ketma-ketligi

Matematikada inflyatsiyani cheklashning aniq ketma- ketligi guruh kohomologiyasida yuzaga keladigan aniq ketma-ketlikdir va spektral ketma-ketlikni o'rganishdan kelib chiqadigan besh muddatli aniq ketma-ketlikning maxsus holati bo'ladi.

Aniqroq qilib aytganda, G guruh, N oddiy kichik guruh va A abel guruhi G ning harakati bilan jihozlangan bo'lsin, ya'ni G dan A ning avtomorfizm guruhiga gomomorfizm bo'lsin. G / N ko'rsatkichlar guruhi ishlatiladi.

A ^N = { a ∈ A : barcha n ∈ N } uchun na = a .

Keyin inflyatsiyani cheklashning aniq ketma-ketligi quyidagicha:

0 → H ¹ ( G / N, A ^N ) → H ¹ ( G, A ) → H ¹ ( N, A ) ^{G / N} → H ² ( G / N, A ^N ) → H ² ( G, A )

Ushbu ketma-ketlikda xaritalar mavjud

• inflyatsiya H ¹ ( G / N, A ^N ) → H ¹ ( G, A )
• cheklash H ¹ ( G, A ) → H ¹ ( N, A ) ^{G / N}
• huquqbuzarlik H ¹ ( N, A ) ^{G / N} → H ² ( G / N, A ^N )
• inflyatsiya H ² ( G / N, A ^N ) → H ² ( G, A )

Inflyatsiya va cheklash umumiy n uchun aniqlanadi:

• inflyatsiya H ⁿ ( G / N, A ^N ) → H ⁿ ( G, A )
• cheklash H ⁿ ( G, A ) → H ⁿ ( N, A ) ^{G / N}

Qonunbuzarlik umumiy n uchun aniqlanadi.

• huquqbuzarlik H ⁿ ( N, A ) ^{G / N} → H ^{n +1} ( G / N, A ^N )

faqat i ≤ n uchun H ⁱ ( N, A ) ^{G / N} = 0 bo'lsa−1

Umumiy n uchun ketma-ketlikni n holatdan chiqarish mumkin=1 o'lchamlarni o'zgartirish orqali yoki Lindon-Xochschild-Serre spektral ketma-ketligidan o'xshaydi.

Manbalar

• Gille, Philippe. Central simple algebras and Galois cohomology, Cambridge Studies in Advanced Mathematics. Cambridge: Cambridge University Press, 2006. ISBN 0-521-86103-9. 
• Hazewinkel, Michiel. Handbook of Algebra, Volume 1. Elsevier, 1995 — 282 bet. ISBN 0444822127. 
• Koch, Helmut. Algebraic Number Theory, 2nd printing of 1st, Encycl. Math. Sci., Springer-Verlag, 1997. ISBN 3-540-63003-1. 
• Neukirch, Jürgen. Cohomology of Number Fields, 2nd, Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, 2008 — 112–113 bet. ISBN 3-540-37888-X. 
• Schmid, Peter. The Solution of The K(GV) Problem, Advanced Texts in Mathematics. Imperial College Press, 2007 — 214 bet. ISBN 1860949703. 
• Serre, Jean-Pierre. Local Fields, Graduate Texts in Mathematics. Springer-Verlag, 1979 — 117–118 bet. ISBN 0-387-90424-7.