Structure of mod p H-spaces with finiteness conditions

2001 ◽  
pp. 103-130 ◽  
Author(s):  
Juan A. Crespo
Keyword(s):  
Finiteness Conditions ◽  
Mod P

Representations of the fundamental group and the torsor of deformations. Global aspects

2017 ◽  
Author(s):  
Ahmed Abbes ◽  
Michel Gros
Keyword(s):  
Fundamental Group ◽  
Koszul Complex ◽  
Finiteness Conditions ◽  
Inverse Systems ◽  
Logarithmic Geometry

This chapter continues the construction and study of the p-adic Simpson correspondence and presents the global aspects of the theory of representations of the fundamental group and the torsor of deformations. After fixing the notation and general conventions, the chapter develops preliminaries and then introduces the results and complements on the notion of locally irreducible schemes. It also fixes the logarithmic geometry setting of the constructions and considers a number of results on the Koszul complex. Finally, it develops the formalism of additive categories up to isogeny and describes the inverse systems of a Faltings ringed topos, with a particular focus on the notion of adic modules and the finiteness conditions adapted to this setting. The chapter rounds up the discussion with sections on Higgs–Tate algebras and Dolbeault modules.

Congruences involving alternating harmonic sums modulo pα qβ

2018 ◽  
Vol 68 (5) ◽  
pp. 975-980
Author(s):  
Zhongyan Shen ◽  
Tianxin Cai
Keyword(s):  
Positive Integer ◽  
Positive Integers ◽  
Mod P

Abstract In 2014, Wang and Cai established the following harmonic congruence for any odd prime p and positive integer r, $$\sum_{\begin{subarray}{c}i+j+k=p^{r}\\ i,j,k\in\mathcal{P}_{p}\end{subarray}}\frac{1}{ijk}\equiv-2p^{r-1}B_{p-3} \quad\quad(\text{mod} \,\, {p^{r}}),$$ where $ \mathcal{P}_{n} $ denote the set of positive integers which are prime to n. In this note, we obtain the congruences for distinct odd primes p, q and positive integers α, β, $$ \sum_{\begin{subarray}{c}i+j+k=p^{\alpha}q^{\beta}\\ i,j,k\in\mathcal{P}_{2pq}\end{subarray}}\frac{1}{ijk}\equiv\frac{7}{8}\left(2-% q\right)\left(1-\frac{1}{q^{3}}\right)p^{\alpha-1}q^{\beta-1}B_{p-3}\pmod{p^{% \alpha}} $$ and $$ \sum_{\begin{subarray}{c}i+j+k=p^{\alpha}q^{\beta}\\ i,j,k\in\mathcal{P}_{pq}\end{subarray}}\frac{(-1)^{i}}{ijk}\equiv\frac{1}{2}% \left(q-2\right)\left(1-\frac{1}{q^{3}}\right)p^{\alpha-1}q^{\beta-1}B_{p-3}% \pmod{p^{\alpha}}. $$

Finiteness conditions and relative derived categories

2021 ◽  
Vol 573 ◽  
pp. 270-296
Author(s):  
Lingling Tan ◽  
Dingguo Wang ◽  
Tiwei Zhao
Keyword(s):  
Derived Categories ◽  
Finiteness Conditions

Table des Solutions de la Congruence x 4 + 1 ≡0 (mod p) pour 800,000 ≧p ≧1,000,000

1960 ◽  
Vol 14 (71) ◽  
pp. 284
Author(s):  
J. W. W. ◽  
A. Gloden
Keyword(s):  
Mod P

scholarly journals On mod p singular modular forms

2016 ◽  
Vol 28 (6) ◽  
Author(s):  
Siegfried Böcherer ◽  
Toshiyuki Kikuta
Keyword(s):  
Modular Form ◽  
Number Field ◽  
Modular Forms ◽  
Fourier Coefficients ◽  
Siegel Modular Form ◽  
Mod P

AbstractWe show that a Siegel modular form with integral Fourier coefficients in a number field

scholarly journals Homological finiteness conditions for a class of metabelian groups

2017 ◽  
Vol 50 (1) ◽  
pp. 17-25
Author(s):  
Peter H. Kropholler ◽  
Joseph P. Mullaney
Keyword(s):  
Finiteness Conditions ◽  
Metabelian Groups

scholarly journals INJECTIVE MODULES OVER DOWN-UP ALGEBRAS

2010 ◽  
Vol 52 (A) ◽  
pp. 53-59 ◽  
Author(s):  
PAULA A. A. B. CARVALHO ◽  
CHRISTIAN LOMP ◽  
DILEK PUSAT-YILMAZ
Keyword(s):  
Roots Of Unity ◽  
Finiteness Conditions ◽  
Simple Modules ◽  
Injective Modules ◽  
Injective Hulls

AbstractThe purpose of this paper is to study finiteness conditions on injective hulls of simple modules over Noetherian down-up algebras. We will show that the Noetherian down-up algebras A(α, β, γ) which are fully bounded are precisely those which are module-finite over a central subalgebra. We show that injective hulls of simple A(α, β, γ)-modules are locally Artinian provided the roots of X2 − αX − β are distinct roots of unity or both equal to 1.

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