Search

9 Nov 2020: The square matrices A and B over the field F are congruent if B = PTAP for some invertible matrixP over F. ... Which, if any, over Q?) Try to get away with the minimum calculation.(.

5 Jun 2020: n1 obtained byminimizing the ideal Shannon code-lengths over the family {Qθ}θΘ,. ... Integrating over distortion-balls effectively changes a continuous alphabet intoa discrete one and log Q(B(xn1,D)) still makes sense as an idealized code-length.

9 Nov 2020: lemma. Since the slope filtration descend to G u(a,b), for a a′ b′ b we have a subquotient over. ... Def (a,b) over s, and Defs(a,b1) to be the fiber of Defa,b1 Def (a,b) over s.

31 Jul 2020: Lemma 13. Let l,a,b pZp and m,c Zp be fixed, subject to the condition that z2 mz c isirreducible over Fp. ... where s is a binaryquadratic form over Fp with a double root over Fp.

9 Nov 2020: separable extension of K. Let G be the Galois group of L over K and let B be the integral. ... Spec(B) Spec(A) has finite fibers. Hint: reduce to the two cases (1) L is separable over.

4 Mar 2020: ii) The group 〈S | E〉 is stable.Proof. Use the fact that dn (cad,cbd) = dn (a,b), and fix for each γ Γ = 〈S | E〉 a word over S1in the ... Define. pn = PxXn ((Xn,x) 'r (B,b)) and p = P(Y,y)µ ((Y,y) 'r (B,b)).

5 Jun 2020: ixs xs. Here B B denotes the algebra generated by B and B and xs xs. ... is the realization over Z n s s obtained by glueing realizations xs and xs.

16 Nov 2020:  : a,b,x Fp. of matrices over the finite field Fp (p prime). ... Which are indecomposable? Remark: Over C irreducibility and indecomposability coincide but this can fail for mod-ular representations.

11 Nov 2020: The key idea is to use theLang–Weil estimate to relate the cardinality of JΣtop to the asymptotic behaviorof the number of points on Xµ(b) over a finite field, as ... Define the group scheme Jb over F by. Jb(R) ={g G(RF L) | g1bσ(g) = b.

3 Mar 2020: Provethat the affine cone over P1P1 in its Segre embedding inside P3 is not smooth. ... Which of the following morphisms separates points resp. tangent vectors?(Assume we’re working over a characteristic 0 field).(a) A1 A2 sending t 7 (t, t2).(b) A1 A2