OpenLLM-France/wikimedia huggingface dataset:
# Grothendieck trace formula

In algebraic geometry, the Grothendieck trace formula expresses the number of points of a variety over a finite field in terms of the trace of the Frobenius endomorphism on its cohomology groups. There are several generalizations: the Frobenius endomorphism can be replaced by a more general endomorphism, in which case the points over a finite field are replaced by its fixed points, and there is also a more general version for a sheaf over the variety, where the cohomology groups are replaced by cohomology with coefficients in the sheaf.
The Grothendieck trace formula is an analogue in algebraic geometry of the Lefschetz fixed-point theorem in algebraic topology.
One application of the Grothendieck trace formula is to express the zeta function of a variety over a finite field, or more generally the L-series of a sheaf, as a sum over traces of Frobenius on cohomology groups. This is one of the steps used in the proof of the Weil conjectures.
Behrend's trace formula generalizes the formula to algebraic stacks.

## Formal statement for L-functions

Let k be a finite field, l a prime number invertible in k, X a smooth k-scheme of dimension n, and ${\mathcal {F}}$ a constructible $\mathbb {Q} _{l}$-sheaf on X. Then the following cohomological expression for the L-function of ${\mathcal {F}}$ holds:
    $L(X,{\mathcal {F}},t)=\prod _{i=0}^{2n}\det(1-t\cdot F\,\,|\,\,H_{c}^{i}(X_{\bar {k}},{\mathcal {F}}))^{(-1)^{i+1}}={\frac {\det(1-t\cdot F\,\,|\,\,H_{c}^{1}(X_{\bar {k}},{\mathcal {F}}))\cdots \det(1-t\cdot F\,\,|\,\,H_{c}^{2n-1}(X_{\bar {k}},{\mathcal {F}}))}{\det(1-t\cdot F\,\,|\,\,H_{c}^{0}(X_{\bar {k}},{\mathcal {F}}))\cdots \det(1-t\cdot F\,\,|\,\,H_{c}^{2n}(X_{\bar {k}},{\mathcal {F}}))}}$
where F is everywhere a geometric Frobenius action on l-adic cohomology with compact supports of the sheaf ${\mathcal {F}}$. Taking logarithmic derivatives of both formal power series produces a statement on sums of traces for each finite field extension E of the base field k:
    $\sum _{x\in X(E)}\operatorname {tr} (F_{E}\,\,|\,\,{\mathcal {F}}_{x})=\sum _{i=0}^{2n}(-1)^{i}\operatorname {tr} (F_{E}\,\,|\,\,H_{c}^{i}(X_{\bar {k}},{\mathcal {F}}))$
For a constant sheaf $\mathbb {Q} _{l}$ (viewed as $(\varprojlim \mathbb {Z} /l^{n}\mathbb {Z} )\otimes \mathbb {Q}$ to qualify as an l-adic sheaf) the left hand side of this formula is the number of E-points of X.
# Elm Hill, New Brunswick

45°37′16″N 66°04′57″W﻿ / ﻿45.621061°N 66.082506°W﻿ / 45.621061; -66.082506
Elm Hill is a community in Hampstead Parish, New Brunswick, Canada. It is significant as the last surviving Black Canadian community in New Brunswick.

## History

Elm Hill was established by black Loyalists from Virginia in 1806, as one of Canada's earliest black communities. Throughout the 1800s, the community enjoyed a period of relative prosperity, as its remoteness allowed the residents to develop their economy free from outside interference. Located on the St. John River between Saint John and Fredericton, Elm Hill functioned well while the steamers plied the river, stopping there to transport people and products. Once the railroad replaced the river as the highway, however, the community's isolation worked against it. Elm Hill had been a self-sufficient farming community until the 1960s, when many area residents moved to urban areas for better opportunities. Those remaining were not able to keep up the farms, and decline set in. Elm Hill once supported a post office, a store, two churches (Pentecostal and Baptist), and a school although those are all now closed.
As of the 2016 census, the area is still home to 25 residents, many involved in small-scale farming operations or employed in government jobs.
The community was previously known as Otnabog (1854–1893), Upper Otnabog (1876–1911), and Pleasant Villa (1911–1933), before the name was changed back to Elm Hill.
# Preston-Gaylord Cobblestone Farmhouse

Preston-Gaylord Cobblestone Farmhouse is a historic home located at Sodus in Wayne County, New York. The cobblestone dwelling was built in 1845–1846, and consists of a 1+1⁄2-story main block and 1+1⁄2-story rear wing. Both sections are constructed of irregularly sized and variously colored field cobbles. Also on the property is a contributing two-story cobblestone carriage house dated to 1845–1846. The structure is among the approximately 170 surviving cobblestone buildings in Wayne County. The house is now used as a bed and breakfast known as the Maxwell Creek Inn Bed & Breakfast.
It was listed on the National Register of Historic Places in 2009.
# Afghan Boundary Commission

The Afghan Boundary Commission (or Joint Anglo-Russian Boundary Commission) was a joint effort by the United Kingdom and the Russian Empire to determine the northern border of Afghanistan. The Boundary Commission traveled and documented the northern border area during 1884, 1885, and 1886.
The commission was accompanied by Kazi Saad-ud-Din as the representative of the Amir of Afghanistan, but the Afghans did not have a real say in the matter. Tensions between Britain, Russia and Afghanistan grew in 1885, especially in the aftermath of the Panjdeh incident, in which several hundred Afghans were killed by a Russian army, witnessed by several members of the commission. From March until September, it seemed likely that this would lead to war between Russia and Britain, with the Commission at the epicentre (Britain controlled Afghanistan's foreign affairs following the Treaty of Gandamak). However, war was eventually averted.
Between 1885 and 1888, the Afghan Boundary Commission agreed the Russians would relinquish the most remote territory captured in their military advances but they would retain Panjdeh. The agreement delineated a permanent northern Afghan frontier at the Amu Darya, with the loss of a large amount of territory, especially around Panjdeh.
Some letters compiled by Charles Edward Yate "describe the sojourn of the British Commission around Herat during the summer of 1885; the subsequent meeting of the joint British and Russian Commissions in November of that year, and the progress of the demarcation of the frontier up to the time of their separation in September 1886; the return of the British Commission through Kabul to India in October 1886; the negotiations at St. Petersburg during the summer of 1887; the final settlement and demarcation of the frontier during the winter of 1887, and return through Russian Trans-Caspian territory in February 1888".

## Members of the Commission

* Peter Lumsden
* Joseph West Ridgeway
* Alexander Condie Stephen
* Edward Law Durand
* Charles Yate
* William Merk
* Thomas Holdich
* St George Corbet Gore
* Pelham James Maitland
* Milo Talbot
* William Hope Meiklejohn
* James Aitchison
* Carl Ludolf Griesbach
* William Simpson
* Havelock Charles

## Publications

* 18 plates of ornamental tiles from the Afghan Boundary Commission (1884)
# Eclypso

Eclypso may refer to:
* Eclypso (album), 1979 Tommy Flanagan recording
* Hernan Arber, a member of the Psytrance duo Mindelight
# Gramoz Pashko

Gramoz Pashko (11 February 1955 – 16 July 2006) was an Albanian economist and politician. He co-founded the Democratic Party of Albania in 1990 and later served as rector of the University of New York, Tirana. Pashko was married to Mimoza Ruli, sister of politician Genc Ruli.

## Early life and education

Gramoz Pashko was the son of Josif Pashko. He was a graduate of the University of Tirana. He received a bachelor's degree in 1977, a master's degree in 1983 and a PhD in 1989, all in economics.

## Career

Pashko was the cofounder of the Democratic Party that was established in 1990. In 1991, he served as the deputy prime minister and minister of economy in the cabinet led by the then prime minister Ylli Bufi. A few months later, he quit the positions and the Democratic Party membership to form the Democratic Alliance Party. Gramoz Pashko decided to rejoin the Democratic Party, undergoing a vote on the structures of the latter. At the last congress of the Democratic Party, Pashko was elected a member of the National Council of the Democratic Party. Pashko also served as economic advisor to several left wing prime ministers.

## Death

Pashko hit his head on 16 July 2006 while diving in the sea in Himara, southern Albania. The Bell 222 helicopter transporting him to Bari, Italy, for medical treatment crashed over the Adriatic Sea. Six people died in the crash: the two pilots, an engineer, a doctor; Pashko and his son Ruben, who was traveling with him.
# Arzila (Coimbra)

Arzila is a former civil parish in the municipality of Coimbra, Portugal. The population in 2011 was 655, in an area of 3.45 km$^2$. On 28 January 2013 it merged with Taveiro and Ameal to form Taveiro, Ameal e Arzila. There is a Moroccan city with the same name, indicating its etymology is of Punic origin.
It is home to the Paul de Arzila, a natural reserve with a large number of species of birds among other animals. Its patron Immaculate Conception is celebrated annually on 8 December.
Population of the civil parish of Arzila (1864–2011)YearPop.±% 1864 308—     1878 328+6.5% 1890 395+20.4% 1900 476+20.5% 1911 528+10.9% 1920 544+3.0% 1930 578+6.2% 1940 617+6.7% 1950 663+7.5% 1960 653−1.5% 1970 706+8.1% 1981 974+38.0% 1991 711−27.0% 2001 728+2.4% 2011 655−10.0% :
# Assured Compliance Assessment Solution

Assured Compliance Assessment Solution (ACAS) is a software set of information security tools used for vulnerability scanning and risk assessment by agencies of the United States Department of Defense (DoD). It performs automated vulnerability scanning and device configuration assessment. ACAS was implemented by the DoD in 2012, with contracts awarded to Tenable, Inc. (then known as Tenable Network Security) and Hewlett Packard Enterprise Services to improve cybersecurity within the DoD. It is mandated by regulations for all DoD agencies and is deployed via download. Part of the ACAS software monitors passive network traffic, new network hosts, and applications that are vulnerable to compromise. It also generates required reports and data that are remotely accessible, with a centralized console, and is Security Content Automation Protocol (SCAP) compliant. The Defense Information Systems Agency's Cyber Development (CD) provides program management and support in the deployment of ACAS. The Army's Systems Engineering and Integration Directorate said in 2016 that ACAS gives the Army "a clear, specific and timely picture of cyber vulnerabilities and how they are being addressed. Not only does the technology streamline processes at the operator level, it also enables broader goals such as the Cybersecurity Scorecard and automated patching for improved mission assurance."
In 2017, DISA introduced the Command Cyber Operational Readiness Inspection program (CCORI) for enhanced identification of operational cybersecurity risks. Tenable’s software license for the ACAS contract was renewed by DISA in December 2018.
# Rise, Fair Sun

Rise, Fair Sun (朝やけの詩, Asayake no uta) is a 1973 Japanese drama film directed by Kei Kumai. It was entered into the 24th Berlin International Film Festival.

## Cast

* Tatsuya Nakadai as Sakuzo
* Kinya Kitaoji as Asao, Haruko's lover
* Keiko Takahashi as Haruko, Sakuzo's daughter (as Keiko Sekine)
* Shin Saburi as Inashiro
* Natsuyo Kawakami
* Yôsuke Kondô as Koyama
* Kappei Matsumoto
* Yukiko Takabayashi

## Release

Rise, Fair Sun was released theatrically in Japan on 27 October 1973 where it was distributed by Toho.

## Footnotes

* 1 2 3 4 5 6 7 Galbraith IV 2008, p. 292.
* ↑ "朝焼けの詩". Kinema Junpo. Retrieved 27 December 2020.
* ↑ "Rise, Fair Sun". Film Affinity. Retrieved 18 March 2017.

## Sources

* Galbraith IV, Stuart (2008). The Toho Studios Story: A History and Complete Filmography. Scarecrow Press. ISBN 978-1461673743.
# Ballingarry (horse)

Ballingarry (13 April 1999 – 16 April 2020) was a Thoroughbred racehorse who competed for owners in Europe and North America. Bred and raced by the principals of Coolmore Stud, he was named for the village of Ballingarry in the southern part of County Tipperary in Ireland. In October 2002, he was sold to an American racing partnership led by Sidney L. Port.
Ballingarry's most important wins came at age two in the Group One Critérium de Saint-Cloud at Saint-Cloud Racecourse in France and at age three in the Grade 1 Canadian International Stakes at Woodbine Racetrack in Toronto. Following his purchase by Sidney Port, Ballingarry notably won back-to-back editions of the Stars and Stripes Breeders' Cup Turf Handicap at Chicago's Arlington Park.
Retired to stud duty, since 2005 Ballingarry has been standing at Charles-Henri de Moussac's Haras du Mezeray in Ticheville, Lower Normandy, France. Died on 16 April 2020.

## Pedigree

Pedigree of Ballingarry :
| Sire Sadler's Wells 1981 | Northern Dancer 1961 | Nearctic | Nearco |
| Sire Sadler's Wells 1981 | Northern Dancer 1961 | Nearctic | Lady Angela |
| Sire Sadler's Wells 1981 | Northern Dancer 1961 | Natalma | Native Dancer |
| Sire Sadler's Wells 1981 | Northern Dancer 1961 | Natalma | Almahmoud |
| Sire Sadler's Wells 1981 | Fairy Bridge 1975 | Bold Reason | Hail To Reason |
| Sire Sadler's Wells 1981 | Fairy Bridge 1975 | Bold Reason | Lalun |
| Sire Sadler's Wells 1981 | Fairy Bridge 1975 | Special | Forli |
| Sire Sadler's Wells 1981 | Fairy Bridge 1975 | Special | Thong |
| Dam Flamenco Wave 1986 | Desert Wine 1980 | Damascus | Sword Dancer |
| Dam Flamenco Wave 1986 | Desert Wine 1980 | Damascus | Kerala |
| Dam Flamenco Wave 1986 | Desert Wine 1980 | Anne Campbell | Never Bend |
| Dam Flamenco Wave 1986 | Desert Wine 1980 | Anne Campbell | Repercussion |
| Dam Flamenco Wave 1986 | Armada Way 1976 | Sadair | Petare |
| Dam Flamenco Wave 1986 | Armada Way 1976 | Sadair | Blue Missy |
| Dam Flamenco Wave 1986 | Armada Way 1976 | Hurry Call | Nasrullah |
| Dam Flamenco Wave 1986 | Armada Way 1976 | Hurry Call | Fleet Flight |
# Economy of Islamabad

Islamabad is the capital of Pakistan and a net contributor to the Pakistani economy. Whilst having only 0.8% of the country's population, it contributes 1% to the country's GDP. The Islamabad Stock Exchange, founded in 1989, is Pakistan's third largest stock exchange after Karachi Stock Exchange and Lahore Stock Exchange. The exchange has 118 members with 104 corporate bodies and 18 individual members. The average daily turnover of the stock exchange is over 1 million shares. As of 2012, Islamabad LTU (Large Tax Unit) was responsible for Rs 371 billion in tax revenue, which amounts to 20% of all the revenue collected by the Federal Board of Revenue (FBR) as of 2012.
Islamabad has seen an expansion in information and communications technology with the addition three Software Technology Parks which house numerous national and foreign technological and IT companies. The tech parks are located in Evacuee Trust Complex, Awami Markaz and I-9 sector. Awami Markaz houses 36 IT companies while Evacuee Trust house 29 companies. Call centers for foreign companies have been targeted as another significant area of growth, with the government making efforts to reduce taxes by as much as 10% in order to encourage foreign investments in the IT sector.
Most of Pakistan's state-owned companies like Pakistan International Airlines, PTV, PTCL, OGDCL, and Zarai Taraqiati Bank Ltd. are based in Islamabad. The city is home to many branches of Karachi-based companies, banks, and TV channels. Headquarters of all major telecommunication operators such as PTCL, Mobilink, Telenor, Ufone, China Mobile and are located in Islamabad.
Being an expensive city, the prices of most of fruits, vegetable and poultry items increased in Islamabad during the years 2015-2020

## Business

According to the World Bank's Doing Business Report of 2010, Islamabad was ranked as the best place to start a business in Pakistan.
# Richard Demeyer

Richard Demeyer (20 October 1890 – 20 June 1964) was a Belgian sculptor. His work was part of the sculpture event in the art competition at the 1932 Summer Olympics. The art competitions at the Olympics, which ran from 1912 to 1948, were unique opportunities for artists to engage with themes of sport and human achievement, and Demeyer's participation highlighted his standing in the art community.
# Arzl

Arzl may refer to:
* Arzl, Innsbruck, a borough of Innsbruck, Austria
* Arzl im Pitztal, a municipality in Austria
# Electronic Securities Information System

The Electronic Securities Information System (ESIS) was Saudi Arabia's stock exchange until it was replaced by Tadawul in 2001. ESIS was introduced in 1990 and administered by the Saudi Arabian Monetary Agency (SAMA).

## History

The electronic trading system is considered the second largest event in the history of the securities trading industry in the Kingdom after the decision to regulate trading in the market in 1984 and then bore the name (Electronic System for Stock Information), the implementation of the automated Saudi stock information system (ESIS) began gradually at the beginning of the second half of In 1990 AD, one of its most important effects on the market was that it abolished the market segmentation, and enabled the execution of dealers’ orders under clear and fair rules. It also provided accurate information about the prevailing offers and requests and the prices of previous deals, which contributed to improving the deal settlement mechanism. The system has been updated in Successive periods, the most recent of which was version No. (9), which entered into force in 1999, after that this system was replaced by the Tadawul system, which is still in operation.
# AMT Coffee

AMT Coffee was founded in 1993 by Alistair McCallum-Toppin and his two brothers Angus and Allan. AMT Coffee was a chain of coffeehouses that were located in airports, hospitals and railway stations.
AMT Coffee was the first national coffee company in the UK to use 100% bio-compostable cups and lids, 100% fairtrade coffee and 100% organic milk, as well as the first to be accredited with the Fair Tax Mark. In March 2011, Ethical Consumer named it the most ethical coffee chain.
In November 2022 it was announced that AMT was being bought out of administration by SSP Group.

## Locations

AMT Coffee had over 50 coffee bars across the United Kingdom and Ireland.
# Ben Hill United Methodist Church

Ben Hill United Methodist Church is a United Methodist Church in the predominantly Black neighborhood of Ben Hill, Atlanta, in the US state of Georgia. It started in 1853 in a log cabin and was called "Wesley Chapel". The congregation moved to Ben Hill in 1926, and when in the 1960s that neighborhood become mostly Black, the church chose to accept that and integrate. By 1974 the church had become predominantly Black, with Cornelius Henderson as its first Black pastor, and the church grew--from 400 members in 1974 to 4,000 in 1986. Under his successor, Walter Kimbrough Sr., that membership increased to 6,000 by 1989, making Ben Hill UMC "reportedly the largest African American congregation of the United Methodist Church". Its "spiritual awakening and phenomenal numerical growth" are ascribed to its incorporation of "African traditions of call and response" and a neo-Pentecostal style.

## Notable church leaders

* Cornelius Henderson, former president of Gammon Theological Seminary; later bishop, and member of World Policy Council
* Walter Kimbrough Sr., former pastor (1974- ) of Cascade United Methodist Church, father of Walter Kimbrough (Jr.)
# 2013–14 Mohammedan SC (Kolkata) season

The Mohammedan Sporting Club, a football club of Kolkata, won the Durand Cup at the beginning of the 2013–14 season. They didn't do so well in the I-League, where they lost 6 of their first 13 matches and won 3. In mid-season Sanjoy Sen took over as coach.

## Competitions
### Durand Cup
#### Quarter-finals

| Teamvte | Pld | W | D | L | GF | GA | GD | Pts |
| Mohammedan | 2 | 2 | 0 | 0 | 7 | 3 | +4 | 6 |
| Kalighat MS | 2 | 1 | 0 | 1 | 5 | 4 | +1 | 3 |
| Army Green FC | 2 | 0 | 0 | 2 | 5 | 6 | −1 | 0 |

#### Final
### I-League
#### Results by round

| Round | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
| Ground | H | A | A | A | H | A | A | H | H | A | H | H | A |
| Result | L | L | L | W | D | W | L | W | D | D | D | L | L |
| Position | 11 | 12 | 12 | 13 | 10 | 10 | 8 | 9 | 7 | 7 | 7 | 11 | 11 |

#### Matches

Mohammedan S.C. results of I-League matches as of 22 December 2013

### Federation Cup
#### Group stage

| Teamvte | Pld | W | D | L | GF | GA | GD | Pts |
| Dempo | 3 | 2 | 1 | 0 | 5 | 1 | +4 | 7 |
| Mohammedan | 3 | 2 | 1 | 0 | 4 | 1 | +3 | 7 |
| Bhawanipore | 3 | 1 | 0 | 2 | 2 | 4 | −2 | 3 |
| United Sikkim | 3 | 0 | 0 | 3 | 1 | 6 | −5 | 0 |

## Squad information

On 17 December 2013 Sanjoy Sen was officially announced as the new Coach of Mohammedan Sporting Club, replacing former coach Abdul Aziz Moshood.
# Gmina Blachownia

Gmina Blachownia is an urban-rural gmina (administrative district) in Częstochowa County, Silesian Voivodeship, in southern Poland. Its seat is the town of Blachownia, which lies approximately 11 kilometres (7 mi) west of Częstochowa and 60 km (37 mi) north of the regional capital Katowice.
The gmina covers an area of 67.21 square kilometres (25.9 sq mi), and as of 2019 its total population is 12,935.
The gmina contains part of the protected area called Upper Liswarta Forests Landscape Park.

## Villages

Apart from the town of Blachownia, Gmina Blachownia contains the villages and settlements of Kolonia Łojki, Konradów, Łojki and Wyrazów.

## Neighbouring gminas

Gmina Blachownia is bordered by the city of Częstochowa and by the gminas of Herby, Konopiska and Wręczyca Wielka.
# Antonio Meucci (film)

Antonio Meucci is a 1940 Italian historical drama film directed by Enrico Guazzoni and starring Luigi Pavese, Leda Gloria, and Nerio Bernardi. It portrays the life of Antonio Meucci, the nineteenth century inventor and supporter of Giuseppe Garibaldi. The film was shot at the Cinecittà Studios in Rome. The film's sets were designed by the art director Pietro Monastero.

## Cast

* Luigi Pavese as Antonio Meucci
* Leda Gloria as Ester Meucci, sua moglie
* Nerio Bernardi as Alexander Graham Bell
* Greta Gonda as Consuelo Ispahan
* Osvaldo Valenti as Giuseppe Garibaldi giovane
* Armando Migliari as Elisha Gray
* Rubi D'Alma as Liliana Montes
* Anna Valpreda as Mary
* Rudi Dal Pra as Ramiro Gomez
* Olinto Cristina as Wilson
* Emilio Petacci as Sam Cloton
* Nino Pavese as L'onorevole Closter
* Gino Bianchi [it] as Parodi
* Aristide Garbini as Fleming
* Oreste Fares as Il medico
* Nino Marchesini as Il presidente del tribunale
* Eugenio Duse as Il giornalista
* Cesare Fantoni as L'avvocato difensore
* Clara Andri
* Franco Barci
* Ernesto Bianchi
* Gildo Bocci
* Vasco Cataldo
* Tullio Galvani
* Bebi Nucci
* Luciano Seno
* Gina Spicchiesi
* Franca Volpini
* Olga von Kollar
# Fatehgarh Gujjran

Fatehgarh Gujjran is a village located in the Ludhiana West tehsil, of Ludhiana district, Punjab.

## Administration

The village is administrated by a Sarpanch who is an elected representative of village as per constitution of India and Panchayati raj (India).
| Particulars | Total | Male | Female |
| Total No. of Houses | 161 | | |
| Population | 732 | 391 | 341 |

## Child Sex Ratio details

The village population of children with an age group from 0-6 is 95 which makes up 12.98% of total population of village. Average Sex Ratio is 872 per 1000 males which is lower than the state average of 895. The child Sex Ratio as per census is 827, lower than average of 846 in the state of Punjab.

## Air travel connectivity

The closest airport to the village is Sahnewal Airport.