𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Projective Representations and Relative Semisimplicity

✍ Scribed by E Aljadeff; U Onn; Y Ginosar

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
175 KB
Volume
217
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

Let R be a local commutative ring and let p be a prime not invertible in R. Let G be a finite group of order divisible by p. It is well known that the group ring Ž . RG admits nonprojective lattices e.g., R itself with the trivial action . For any 2 Ž . ␣ element ␣ g H G, R* one can form the twisted group ring R G. The ''twisting problem'' asks whether there exists a class ␣ s.t. the corresponding twisted group ring admits only projective lattices. For fields of characteristic p, the answer is in w Ž . x E. Aljadeff and D. J. S. Robinson J. Pure Appl. Algebra 94 1994 , 1᎐15 . Here we answer this question for rings of the form ‫ޚ‬ s, s G 2. The main tools are the p classification of modular representation of the Klein 4 group over ‫ޚ‬ and a 2 w Ž . Chouinard-like theorem E. Aljadeff and Y. Ginosar, J. Algebra 179 1996 , x 599᎐606 for twisted group rings.

📜 SIMILAR VOLUMES

Twists of Galois Representations and Pro
Twists of Galois Representations and Projective Automorphisms
✍ Siman Wong 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 175 KB

We show that two surjective \*-adic Galois representations which are \*-adically close near the supersingular primes are equivalent up to a twist and a standard automorphism of GL n . In particular, two elliptic curves over a number field which are locally twist of each other in fact differ by a glo